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So many real estate agents get a license and think they’ll make large sums of cash. Agents get in, sell a friend or family members home, starve and drop out to a part time job and rarely get back in. Happening a ton with photographers as well. Ebay always has Showcase your website? Free use of Asteroom Professional Subscription Plan 9. I am working on that part next Marketing for Realtors??

Looks like you are in Buffalo. Joining Multiple Buildings with Asteroom. Tours can be crafted with far fewer images. That said, take a look at this Your monthly plans still need to help with costs to fund your tour slot plus other slots not currently being used. Fund the plan, compete with Matterport is stepping on MSPs again, trying to sell direct to our clients. Example 1. Introducing the Matterport Pro 2 Camera Scan YOUR job site Inman 10 Sept. Past Clients 2. Pipeline 3. Colleagues 4.

Vendors and ancillary partners 5. Friends and family Dan — The Inman article is lengthly commentary. I encourage you to subscribe to Inman to How Asteroom got me to switch from Matterport. We have shot more than 2 dozen properties since we recently implemented this. Our realtors are much happier with the time savings since I can shoot any house in 15 minutes or less.

I have yet to hear a buyer state that “This tour wasn’t immersive enough”. IN fact, most buyers are layman in terms of cameras and cannot tell the difference. A matterport has consistent misalignment issues in post and it often Question of the Day: Does your shoot include 2 or more Add On services? Such as: 1. Photos 2. Video 3. Zillow 3D Tour 5. Floor Plans 6. Drone Photos 7. Drone Video 8. Twilight 9.

Virtual Twilight Why is the ‘we-get-around’ forum so incredibly spammy on email? So in summary : my mistake! Question of the Day: Should you get paid at closing? No closing; No pay? Whichever comes first. You can accomplish this through most payment platforms, such as Square.

This option also gives an opportunity to touch bases with the agent. I “follow” the listing you can do this by including it as a favorite listing on Is that a business – or volunteer – opportunity for you? Matterport Pro? It included 54 panos – 13 of which were exterior panos.

The of panos will vary by project – for example, large open spaces will require fewer panos than individual offices with connecting halls, and complex layouts.

If you are shooting with a relatively low resolution camera, you will need substantially more images to capture a decent level of zoom in detail, especially of larger rooms. A Theta Z1 would How to Join the Asteroom Photographer Network free for potential leads. Sounds like we are talking about two different things. Or, let me try to say a different way. Every time that you do a real estate photography shoot, do your clients engage you to do a Matterport tour? Thanks, Dan.

When you are starting out, or even if you have been in business for a while, it seems like it makes sense to come in at a lower price point and “steal” business from your competitors. This is not a good practice for a number of reasons. If you are competing on price, everyone loses.

By offering a low price, you devalue Lowest cost Matterport 3D provider in the US. What do people charge these days for Matterport? I feel like I might be charging too much, but without continuing the discussion I have to rely on the search results I see and I feel like those could be misleading. It’s likely that half of all real estate agents that would like to use Asteroom would like to engage a Pro to shoot. For real estate agents to find more sellers, then need to emphasize their virtual marketing services.

That’s you!!!! Knowing that finding home sellers is a pain point for real estate agents during the pandemic, are you encouraging agents to emphasize their virtual marketing services? That’s you!!! For more on this topic, please see Mattervids is another great option, as it gets rid of the UI.

Matterport is being really slow at providing any info, but I was wondering if you or the community came across any success stories and any financial metrics that would help? This is the exact Facebook Lead ad that I ran for Realtors who wanted facebook lead generation for buyer leads, and I Offering Campus Tours? It’s a valuable lesson and will make you smile. Webinar: Ultimate Canva Masterclass for real estate social media marketing.

From the Redfin YouTube Channel: “Your local Redfin real estate agent will price your home right, so you sell for more than the one next door. Add On: if your real estate agent clients only engages you to shoot photos.

Ideal, actually! And no hosting cost!! Question of the Day: Your Matterport special offer for first time clients?

Commercial space, etc. Projecting tours on walls projection mapping. Question of the Day: Longest time between quoting project and engagement? Wayfinding Strategies. Inman: Want more good buzz? Put in your email signature and whenever they praise you send them the link.

Robot virtual tour guide. Why not add a virtual robots within a normal Matterport showcase page, it will look like the one you mentioned in your topic. But a 3D object that be added to the Matterport showcase to be a robot guide for showcase viewers. This virtual robot can be added by Matterport SDK bundle. ADA Compliance is not a scam here is why. First it’s not expensive to start NONE of the instances you want to bring up had tried in the first place.

In another post I made here I told you how to do it Idea: Custom Face Masks with your brand? Or, your clients’ brand?

Just want to Celebrate. How do we see the 3D Virtual Reality Future – where we right? Thanks for sharing. Businesses, restaurants, hotels, schools – it’s so perfect. Persuading them is harder, but I am building up a good set of examples. There is also high demand for tours of yet to be built properties.

Please share it here or start a new discussion. What is your most successful marketing tactic? Want to know more Do you own the organic Google My Business real estate in the top right corner of Google search? Open productpage inside thetour likein 3Dvista but in Matterport or similar. Some of them like the hosted tour if they do private events and such, Some just want me to publish to Streetview and call it a day.

Showrooms are also good. I just got a signed contract to build a tour for an outdoor furniture Real estate office agent meeting: what would you pitch in 10 minutes? You might want to use some of the Inman information he brought up : DanSmigrod private msg quote post Address this user plus 1plus 1plus 10 Inman 24 June Stop letting strangers into your listings!

And it’s true. You can do that. What they do not understand is that the market has changed and the focus is now on the online audience. They are the ones buying most of the properties. You need to convince Realtors this sells houses in today’s market. Especially in today’s market!

It could not be a better time for This post was inspired by the Barnes Creative Studios Do you have a preferred CRM to recommend? Salesforce, Hubspot? I forget who they partner with Their DNS is cheap and bulletproof and auto-configured when you use them for registrar. Fair warning, it is a very technical tool. Their hosting is very good too, but you need to know how to manage a server.

Otherwise you are better off with someone like BlueHost. Top Producer is one I’ve heard a lot that is subscription. But part of what they pay the broker percentage for is things like that. I’d say check and see what’s non-subscription first as getting into real estate is incredibly tough. I’ve tried Captur3D and used their deliverables and their delivered analytics. I also see where it can be used at the listing presentation.

And this is a real estate example. And so the media player, I described it quickly before, but it’s a way to combine multiple forms of media into a single player that can be embedded on any website. So this This version supports multiple currencies any , the purchase of multiple e-tickets in one transaction, and a ‘free demo’ setup option that 3D Technicians can use to demonstrate the possibilities to venue hosts.

Coming really, really soon! Converting Matterport to Video. Software system used? Tiered Matterport Packages. Not really worth the time. When matterport, Inman or WSJ reports this please post here. Anyone going to inman now try to ask this to a bigwig on video? What is your pricing strategy for charging for Matterport tours over time? Since Matterport has changed to 25 or 50 or whatever active sites, how are you handling the realtor charges, do you have a set time frame.

Or, are you moving away On going saga for Matterport. Google My Business listings fall into two categories. As the data is unverified Google rank it lower on the scale. Once someone claims the Do Realtors Think You’re “Cheap? Explaining the difference between a virtual tour and a slide show. Join , Die or Migrate We are all in this together, so we have a large “eco system” to beat back their attempts to control OUR businesses. Thank you Dan for putting this together so we can freely share and learn from each other what needs to be done.

Anyone want to buy a After-all, any buyer has at least 5 ways to cancel the contract and get their earnest money returned. So, get under contract to tie the property up, do your due dil and inspections, decide for sure you wish to proceed with the purchase. Everyone’s happy! Realtor states MP tour too complicated. I’ve been training agents for 30 years. Theres a reason real estate technology lags years behind other sectors.

Focus on the agents who get it. There’s plenty of agents who focus on the populations who do crave these tools, And the rest will get it, Or not. I am 60 years old. I just don’t feel the need for it anymore. If you are a younger person starting out, more power to you. At this age, I value having my weekends. If a great client asked me to do a shoot on a Saturday or Sunday and had a good reason, I would do it.

We are in a time period when people send a message, they expect a reply right away. Have you done a Matterport of a messy house or? I can’t really share the model I shot Friday. Ah yes We call them “collectors” in the insurance world. I like that term. Whatever they collect it’s important to them I’ve been in houses where the whole house was 4 feet deep and there was a path through it, but not with my Matterport.

Golden rules apply They have submission forms for their clients, but obviously they have no other contact information. Any tips would be greatly appreciated! Sponsoring a Pitch Meeting for Brokers. I am looking into becoming an affiliate. All the meetings are being done virtually for now. I guess it’s time I start working on a powerpoint. Pricing for commercial scanning, matterport? Zanzucchi with 3D RoomScapes. This show will inspire you. Sell 3D marketing as tool top get buyers first to offer technology.

Question of the Day: Do you get Shout-Out video testimonials while on-site? Perhaps someone here will review SoTellUs app and suggest a much better name 😎 for it! Case Studies: how to get them from clients? The best time to do the smartphone video is while you are on-sight at the end of all your work. For ongoing clients, you may find that that are willing to do a shout-out video that talks JamesDuffy ifti. It’s interesting. I know about the toggle for the 3d floorplan.

I toggle the Eyespyplan Autostart ‘On’ so that when the tour starts, the 3d model is the first scene. Gives a sense of “coolness” when the tour starts. When you do that and go back to the tour, the 3d floor plan doesn’t show up in the bottom left Guess I think I prefer having the 3d floorplan at the bottom left, unless Eyespy adds that in eventually.

That’s great. How about text? I think I need to shut up I bet eyespy staff just nodded their heads till I get my own and play with it. When I do I will check on your branding Question of the Day: How can you get home seller leads to give to clients?

Something like eyespy? How great is that? More spam for my inbox. This one picked the first two. Dan Smigrod making things fun since that you can use today to get more. Very interesting. They could at least outfit their employees with cameras.

This is nothing more than a Facetime chat with an agent. Question of the Day: Phone ringing off the hook to order Matterport Tours? Can you ask a different way? EyeSpy Marketing material. Virtual Showing within Tour. I have been talking to clients about it but don’t have a solid example yet.

I would share credit, etc. Some realtors have a solution — the virtual tour,” reports Newsday. Considering 3D Virtual Tour Business. I see the discrepancy in how you feel about pricing has a lot to do with where we live. I’m not sure if it works in Australia, or whatever part of Australia you are in. It’s about all about the No jobs, no calls nothing since March 17 harry.

Zillow – Capturing free, easy 3D tours. It’s getting there but slow moving. Hope you are well. Virtual Open Houses: Are you working with agents to provide this?

Better to have one photographer shoot the home, in order to allow numerous others see the property, than allow people to view homes. Agents and anything RE related are considered essential here in MD. Matterport: the Irony of Competing with Pros. Enjoying the rush of business? Don’t and here is why. This is a unique moment for us and we need to learn and advance while we’re stuck at home.

Going forward, many more people will be asking agents “will you be doing a virtual tour? I got a call today from an agent I don’t know.

Here’s how it As the service is made on a weekly basis I think it’s different than a regular capture. I think we can go on a recurring fee on a monthly basis.

Does James gave you some north on it for us? Many thanks. Who’s including Zillow 3D tours with your services? I just did not know if you needed to attribute the tour somehow to the listing agent, but it goes with the property, not the agent. Knowing how to have a virtual open house with the agent live and able to talk to the buyers is crucial.

It gives buyers special access and answers to questions without waiting. It also adds value to the I am NEW in Matterport. What was your major mistakes and wins?

Collecting 3rd party articles about 3D Virtual Reality – Have any? Sink or Swim? Putting Matterport Tours on Apartments. But Costars also owns the following company: Apartments. Unbranded Matterport Tours. Great 3rd party video to help you sell Matterport. In today’s video, I’m sharing ideas for Realtors to keep their business going, even with Take an online course! This one is free! Do you see any conspiracy against virtual tours in the following situation. IN one home they installed a smaller shower base and decided to frame in the shower wall around that, so there was an additional almost two feet of dead space inside a wall cavity that was easily knocked out to make the shower that much wider!

Point is not trying to preach to the choir that the Working for an exchange of services Consider though that there are tax implications to barter. We had a barter exchange club here locally – EVERY member ended up getting audited for TY , some having to pay additional tax, penalty and interest. Don’t know the particulars beyond that, just be careful and document, document, document.

Best, Keith. View from Your “Matterport Office”. When the Matterport tour of this large space is ready, can you start a new discussion with what you learned from doing such a large space?

A Matterport 3D Tour can save real estate deals trying to close on lockdown. I have saved two deals in last 2 weeks because the agent did not know; used my advice and saved the deals. If you had a Matterport 3D virtual tour done it automatically gives precise measurements. If you are the buyers agent ask seller agent and it might save the deal Dan — Hi Dan, Hope you and your family are staying safe and doing well I am still a bit confused on how I can add a Matterport tour to my Constant Contact eblast.

Because of the virus we have been doing How to get potential in-bound leads from Apartment Communities. At 1 pm ET this Can this allow the agent to switch view to other properties with the client s still there? I have been informed that there is something coming out that does that. I use it frequently for video chats. Be safe, Dan. Replaced by Virtual Open House? Real Estate Broker: [Matterport] “seals the deal with the listing”. Or, to get a similar shout-out testimonial video from one or more of your clients?

Inman: Northwest MLS halts open houses amid coronavirus crisis. Inman: Coronavirus drives adoption of virtual tours and Video. You are helping people! Then if they Thank you. Facebook offer ad grant for businesses affected. This is going to be extremely helpful for some of the hardest hit industries, like restaurants, health and beauty, gyms, etc. I could Matterport jumps on the Coronavirus bus. Obviously, as Matterport Service Providers, we would prefer that Matterport create the demand with the call-to-action to engage a Pro.

On a tactical note, I am super-surprised Matterport would use that geeky, spider-web artwork to try to communicate an immersive, walk-around Here is the link that we used during the show People still leave their normal lives going to work, shopping and parks.

If it turns into something really ugly so people prefer to stay home nobody will be buying properties. So, how do you overcome this objection? Video: How to accept a deposit to confirm a Matterport shoot. See the Castle example above for the best walkthrough style you can achieve.

It’s not as extensive as Matterport. I used their web app to build this tour, not the mobile app. I have the mobile app and it seems to work very similarly, but I have not tested it. What to charge residential builders for Matterport? I have one client that gave me homes last year, and he’s on track to double that this year with his expanded team.

The deal I have with him, and him only, is that that I don’t bill by sq ft, I bill by number of scans. I have a flat rate for any homes up to 99 scans. If it’s over scans I charge an additional fee for that. I explain how Matterport pricing works and I basically How might you use this Matterport marketing video to help you get more Matterport Service Provider Question of the Day: How are you using Instagram for your Matterport biz?

The Community Podcast Ep. Matterport Measurement Mode Announcement! I don’t understand this new pricing structure as it does not benefits me as a service provider at all. I have tours that I have to keep them active for a very long time, yes the client paid me a premium so it justifies hosting them for them. Who has the time to send out hundreds of invoices a month for coins for hosting its a waste of time, chasing clients for these payments? We need self-hosting option yesterday This is purely meant for just quick organization.

Best camera and tour software for inventory building. With another camera model such as the Insta cameras – but there are many more – you are independent from Matterport and can copy the tour wherever you want.

Any hosting provider will be OK, although some Virtual Tour hosting companies offer additional services, such as more or less sophisticated software to compose I like the background music too, it fits very well. Can you share how you blended the video file to the Matterport Tour? I am new to this but I can’t see how a client wouldn’t love your work, I am very impressed, Jim. You get wp3dmodels free.

Glad you are bouncing back from your health challenges. How to Shoot, Upload, Free Tour Giveaway: Promotion for Agents? How do you collect payment on Matterport Tours, Photography, Video, etc.?

Glad to hear. Help Needed: Review and recommend changes to EyeSpy marketing piece. Recently, I asked Andrew, CEO of EyeSpy, if he might put together a marketing piece to assist us in selling these services to prospective clients.

The following link contains 2 files: affremedia. Marketing Matterport: What if you could [benefits]? You can! Here’s how Vid: Imagine getting paid more than commodity pricing for Matterport tours!

Transcript: S. To take Wingman’s comment just a bit further, it would be great to create a working group of some sort to create the “ideal” generic scripts, which could then be made more custom depending on the situation.

Virtual tour website and showcase platforms. Question of the Day: What differentiates you from other Matterport Pros? All, This is likely the most important Question of the Day – this year. Knowing what differentiates you – and communicating to potential and existing clients what differentiates you – will help you get paid more than commodity pricing.

What differentiates you? Enjoy your weekend, Dan. No need for After Effects, though it’s also a great application. The top window of my current website has a video of a Matterport walkthrough – Home3D. Question of the Day: What is the one objection that you hear most often? Looking forward to hearing the first 45 minutes. House I was shooting was in a dead area for cell service.

Creative concept: – The year of digital twins. I take it slow in the video to explain each step, but you should be able to create and customize each project in a couple short minutes once you know what you are doing. In the video above I created the following deliverables page, property website, and media player.

You will notice my logo and branded background color. This will match your branding as well once you have it set up. Since I am located in Kansas City and kc. Here are a few example projects I have under You can directly and easily place orders now on our website here! Why do real estate agents do Open Houses?

That’s why I include a stand alone 3D Tour set to music on a continuous loop, with all my jobs. Many of my clients set up their laptop or tablet at the open house and just let it run all day. They say it helps to show that they use the best technology to market and sell their homes, and it works.

Almost all say the 3D tour on display has greatly enhanced their open houses. Is it possible to add Matterport tours to Vimeo?

Thank You, Marshall. More remarkable is that this state Alabama is a so-called “buyer beware” state where buyers Question of the Day: What is your minimum work order? But, even for those I do not I takes the extra steps to make sure that the services in which I provided are being used to their fullest potential. My takeaway: Every real estate agent using Matterport should be doing a media release like this! Selling tactics for Business tour services.

Why Choose. Get more listing presentations 2. Win more Tip: Do you have a “use it [budget] or lose it” year-end corporate client? Between now and 31 December , I urge you to reach out to your corporate clients to see if they want to pre-paid for Matterport scanning before the end of this year.

You do not even need to offer these clients a discount for pre-paying. Plus, simply ask them the amount Video: What is the value proposition of a real estate agent? It may help you define your value proposition. For example: Value Proposition 1: I am a real estate photographer. And, for out of state, or out of country buyers, it’s a must have for sure. The only way that happens is because of some competitive situation, or that the listing agent A transcript of this Short Story appears below.

First, some backstory. My vision for your Matterport Service Provider business is that one day, you will land a trusted client that will want to place one order for Matterport A great way to promote your brand across the web as your clients display and share the player. Which is also great for SEO purposes! Screenshot below showing you the location of where your business name would be with a link to your website.

Using Matterport to document a client booth at an event. Plus, Ricoh Theta Z1 makes the capture faster and less intrusive. And, thanks for sharing! Matterport Marketing Newsletter: Friday, 13 December It’s also another reason why they should purchase a Matterport Tour over so many other platforms offered by 3rd parties. The implications of this new feature for all business verticals is a really big deal!

Why home buyers will want to buy the 3D Tour created to sell the home. Very nice! It appears there is no measurement support for ‘s which may be part of a tour. As well, if desired, one could add measurements to floor plan mode in Workshop, publish the changes and have those measurements be viewable to the public. In any case, this change Happy holidays, Dan My question is how difficult is it to remove virtual tour from Google streets if the client decides not to continue?

Are you a Real Estate Agent thinking about getting started with Matterport? Advice for a beginner. Simply Private Start with a free account here: admin. MSPs: How to get more Matterport biz from winter storms and at full-price. How to demo your Matterport tours – to a potential client – without WiFi.

If there was any award case for Best Click-Bait advertising MP definitely got my nomination. Realtors in Ca. The Ca. For many of us in the midwest, the winter months are slower so this allows some cashflow in a cashflow strapped time.

You can do this anytime before the end of the year and tailor it to what you offer and your own needs. Being in the youth sports industry, there is an industry disrupter right now called Photoday. Instead of parents paying for the photos in advance and getting whatever they get, they now have the chance to see the Happy Thanksgiving, Dan.

My issue remains to be that realtors don’t know what to do with the tour once it is done. They put it on facebook and that’s about it. I have suggested ideas such as making a QR code to hand out at the open house thanking the potential client for visiting and allowing them to re-visit the house virtually. I’m always met with resistance usually with the thinking that they want the client to Ben Claremont on: Successful vs. Unsuccessful Virtual Tour Photographers.

Matterport tours I believe become much more powerful when used or shown on a mobile device. So, many people have only really seen an older Matterport tour on a computer interacting with the tour with a mouse and think I have seen Matterport and that doesn’t work for me.

Once you let them interact with a tour on an iPad preferably I heard he is knowledgeable about 3D stuff. What a week! Got one that you would like to share? Question of the Day: What business development strategy works best for you? Changes in Marketing. It is my understanding Mr. I remember the discussion about one of the better known Ambassadors leaving Chris H.

It is my understanding Ambassadors receive inside trade information before the rest of the MSP network, and benefits from their participation, such as advising on future company Please tag: uavexpo19 Best, Dan.

Side-By-Side videos before and after of Matterport. Matterport Tour Lead Capture. And MpEmped has extra layers sitting on top on a model to make all its menu things. Ever lost business because you were too slow to respond? How to solve this!

I haven’t tried to use a 3D camera yet in my business. I don’t see how that would help. I need a remote control robot to do that. So it will take some time before that happens. Cupix Care – more than Matterport.

Marketing strategies for selling zillow 3D Home Tours – I need help. I’ve had incredible resonance with my clients with the Zillow 3D Home – NOT because of the beautiful photography it’s not , but because of the advantages that it achieves. Let them know that for 1 week, they have preferred search placement, the home gets extra email blast treatment, etc. Get the exact facts from your Zillow contact and pitch those Matterport must have pissed Zillow off :. You nailed the navigation in this beautiful space.

Facing objections by realtors. It accelerates the decisions making process. I had the other one pinned to the top of the feed for the last few months. I just switched to this one the other day. Another great benefit to the membership. Question of the Day: 1 objection you receive about doing Matterport Tours? How do you handle the objection: We want people coming to an open house I always tell them that 3D Tours will bring more qualified buyers to the open house.

I also give the agent a copy of the 3D Tour with music on a continuous loop that they can let run on their laptop or iPad during the openhouse to show potential buyers that they use the latest techkno;gy to market their clients home. That’s something most had never thought of and when they hear it, a light bulb goes off in their head.

How do you handle this objection: “There isn’t any privacy in the tour I do not think it is any of a privacy concerns. It is just an excuse not to use tours, probably because they will show vendors that even an agent can be replaced with a tour.

We have scanned some expos in the past in exchange for an exhibition stand at the expo. Question of the Day: What is your close rate? Seeking somebody who can create promo video from Matterport Tour. Get noticed and grow your brand. No many people realize that it’s simple to get noticed.

Let say you have a contract to scan a property; you go through your checklist: camera, tripod, battery charged, iPad charged, business card, etc.

You get into your car and drive to the property, stopped by the gas station, the tank is full, grab a bottle of water and continue. You arrived at Research: The Matterport 3D Tour likely pays for itself! As asserted in my last post, I do not believe that any knowledgeable buyer will overpay for a property solely due to the availability Homes marketed with 3D Tours sell for more in less time.

Question of the Day? Do you offer Aerial Photos and Video? Matterport App Sample. No question about that. My motivation was to not lose money, while attempting to keep pace with the competition, most of whom do not charge for hosting now, but may in the future.

This said, if I only have 12 spaces up and backed up by paying Realtor Websites and Matterport. That’s great! Matterport seamlessly integrates with realtor. Agents Request Tweaks and Features. Post it on FB and boost the post. You pick all the demographics. The cost is very low. If you have an Instagram account, it will also place the post there and boost it.

To be real estate industry’s tech leader”. If you are a Let Kevin show you how a deeper understanding of the home selling process and how real estate professionals can fit into your process. Question of the Day: Do your clients ever ghost you how do you overcome?

Flooded with emails, texts, WhatsApp etc. Sometimes emails end up in spam boxes. If they are worth keeping, just always keep calm and polite, try again after a few days or, probably the best route, pick up the phone and call them. That brings us up to current times.

Many high schools require students to take three years of math during their four years of high school in order to graduate. There is considerable pressure to have all students take an algebra course. The nature of the instruction and the learning in many of these math courses follows the “percent on step 2” that has been noted above. Students are now learning the underlying concepts, or how to make use of the math in other courses or outside of a formal school setting.

The language of Mathematics does not consist of formulas alone. The definitions and terms are verbalized often acquiring a meaning different from the customary one. Many students are inclined to hold this against mathematics. For example, one may wonder whether 0 is a number. As the argument goes, it is not, because when one says, I watched a number of movies, one does not mean 0 as a possibility.

But do not forget that ambiguities exist in plain English the number’s number is one of them and in other sciences as well. As s matter of fact, mathematical language is by far more accurate than any other one may think of. Do not forget also that every science and a human activity field has its own lingo and a word usage in many instances much different from that one may be more comfortable with.

As a final note in this subsection, the 4-step diagram represents only part of the field of math. For example, it does not include math as a human endeavor with its long and rich history. I did understand your “Zero Saga” and I agree wholeheartedly that dividing by zero is completely meaningless.

This works for every number except for zero, which isn’t exactly a number. Zero is a number, and a concept for “nothing. Try to break an apple into zero equal parts!

I thought of the question that you asked, “Try to break an apple into zero equal parts! If you have 1 whole apple and you attempt to divide it into 0 equal parts do you not still have 1 whole apple? Have you really attempted in doing so? I am sure you failed, Right? So do not conclude anything. I always saw this as the number of times something can happen out of the number of possible variations of what can happen.

Out of 0 events an event happening 1 time is just erroneous and invalid. It seems apparent that the zero paradox should be broken into to areas: mathematical and physical. Not only is the need to define zero, but infinity as well. For some it is not a question of whether it exists, but merely what the definite result is.

I do agree with you that one must make a clear distinction between the abstract concepts and the concrete concepts as well as their useful implications in modeling process of reality. Therefore, one must engage in investigating mathematical knowledge, especially the relation between conceptual and applied procedural knowledge.

The distinction between these knowledge types is possible at a theoretical, epistemological and terminological level. One may classified them according to their different approach to a given problem:.

Applied knowledge: How to get from where one is to where one wants to go in a finite number of steps. Conceptual knowledge: How to get from where one is to where one wants to go in a finite or an infinite number of steps, or a leap without any steps at all.

An example of conceptual knowledge would be Where one is: natural numbers Where one wants to go: the end of them How: Infinite number of steps.

For the applied knowledge it would be Where one is: natural numbers Where one wants to go: the end of them How: In a finite number of steps depends on what calculator you are using. As you see, conceptuality is subjective while realization is objective.

Most conceptuality is metaphysical; while reality is mostly physical. Now with respect to the last part of your comment, “what the definite result is”, one must recall that: being definite has the property of being definable. What one can reach is finite, thus one can never reach infinity, therefore forget its beyond!

Now, according to the Einstein’s theory of relativity, nothing in our universe can accelerate up to the speed of light. Only, under this critical hypothesis i. Like any mathematical model of reality, this model has its own restriction s. For example, considering you travel with speed of v, then for each second that passes for you, the clock of the observer, registering. By violating this condition, i. It is unfortunate that, you violate certain rules and as a result of you own action, you are siting and wondering why and how!

You are not alone, on this phenomenon and its many manifestations in our lives. Truly fascinating argument. For those that argue that infinity is a correct answer, how can they explain that calculators, typewriters, and computer keyboard do not reflect the infinity symbol?

I have comments on two issues. I am waiting for your valuable comments. We can SEE the “infinity” in our own eyes in broad day light. But, the result is not unique–i. Therefore, the problem lies in the “nonuniqueness” of the result, so that it is not “consistent” which assumes unique mathematical value amongst all the cases.

Repeating this operation again and again is nonsense. Once is enough, right? Otherwise eventually you get tired of counting this repetition, beyond that is infinity which you have never reached. The problem is in the measurement calculation, not the outcome. That is, there is no error. Your Web site defines such a calculation, showing that some people forget that they are not dividing by zero, but dividing by an error.

I could understand exactly why they were so adamantly arguing with you because we have been brought up to believe you can indeed divide by zero. However, your examples disproving the division were very persuading and I found myself smiling as individuals got more and more upset as you proved their childhood lessons were indeed fallacy I guess it shows how unwilling we can be to changing our old ways of thinking You are right.

Correcting our habit is much harder than learning something correctly in the first place. Habits are indeed the “gravity” of mind. One must be aware of this very formidable and attractive force. What we see is how difficult it is for many of us to correct the habitually wrong conceptions than learning them correctly.

What we should do as with anything else is rethink the concept for ourselves. We must be willing to change the way of thinking, the courage to see things differently, and not be stuck in a gravity of the mind situation. I am very curious about this development because I foresee it to be the precursor to the next big break through in applied and theoretical mathematics.

I can not seem to find an inkling of research out there. I have in two instances in my life come across it. The first was my first year calculus teacher who told the class his research was just that and the second the infamous Tycheon. Any information or help you could provide would be greatly appreciated. I understand your feeling of frustration. There have been many attempts, however, unlike the established applied numerical systems such as complex numbers, these new systems are merely “abstract” with no application.

As, you expressed well, within the current concrete numerical systems; the act of dividing by zero is meaningless, thus forbidden. Another interesting observation is the use of the word zero in Sri Lanka, which is probably a cultural thing. Using the word zero rather than naught. For example, in the UK we rarely use the word zero. If we were giving out a phone number, we would usually say, my number is oh seven The British Telephone directory enquiries service never uses the word zero, always oh.

The way I see numbers is rather simplistic. The smaller the number you divide by, the larger the number you get. An infinitesimally small number on the bottom of a fraction will result in an infinitely large result. However, that infinitesimally small number is still a number. Zero denotes nothing. If you divide something by nothing you have NOT divided it. You are right in stating that ” If you divide something by nothing you have NOT divided it. Albeit, stating that any defined number divided by zero is infinity is not incorrect.

You are questioning ” conventional way Again how do one define convention? In real analysis, between any two consecutive points there is another point – leading to the statement there can be infinite number of points So do we say there are “Undefined points??? In my humble opinion, anything divided by zero can be said to be infinity and zero divided by zero is indeterminate!!

The main problem I have with this line of argument is “the act of dividing by zero” which is meaningless Therefore, it does not make to ask further what is its result, whether it is indeterminate or not. Mathematical conventions are created for unification of our usual arithmetic operational rules, in most cases. You are right in stating that ” Which means there are innumerable and even uncountable number of points within this non-empty dense set.

It does not say exactly how many. Infinity is a concept not any specific number, therefore one cannot do any kinds of arithmetic operations on a concept nor include it in any arithmetic operations. You are certainly entitled to keep ” Really enjoyed your article and comments. As I pointed out earlier. Infinity is a concept not a number. Do you understand the difference? As I stated before, conceptuality is subjective while realization is objective.

It seems you are a believer of infinity as a number and also a believer that you can reach the limit, and thus missing an important distinction. Approaching is different from reaching. Whatever you reach is not a limit. Therefore, you can take a limit, however you cannot “take it to the limit” as in a popular love song the lover is wishing for.

If you can, then it is not a limit, it is merely a numerical functional evaluation. What do you think about this? The paraphrases from your teacher, such as “jumps off to infinity” and “the line curve?

This is so because they cannot be quantified. Now let see where the problem is. Notice that, you graph misses the other part of the function, which is in the third quadrant, symmetric to the part you already have around the origin, for negative x values. Right Chris? As you see this function is not continuous. That is, to graph it you have to lift you hand from the graph paper to draw the other part. Ball [] interviewed 10 elementary and 9 secondary teachers, asking, “Suppose that a student asks you what 7 divided by 0 is.

How would you respond? Why is that what you’d say? It’s just something to remember,” but gave no further justification when probed. Some of the teacher who only gave the correct rule were math majors. Klinger, the author of a book titled ” Mathematics for Everyone “, which is translated into almost all the European languages, and read by most old-timer educators, wrote:.

We do not wish to conduct a philosophical discussion on “infinity” and shall confine ourselves to saying that, if we make a divisor a smaller and smaller decimal value, the quotient will become infinitely great.

Yes, we mean zero. Why not? Let us apply the division of 2 2 by 2 2. Now, the division of any quantity whatsoever by itself for example, the division of 4 by 4 always yields 1, so what we may state the following important rule: Any value arithmetic or algebraic taken to the power zero is equal to Clearly this must not be taken as a proof of “any value Moreover, what about 0 0?

Is it one too? When 0 0 came about? What is its value? One may ask when and how 0 0 became equal to 1? Since the right-side limit of X X as X approaches positive-zero is one, but its left-side limit does not exists, therefore, one concludes that 0 0 is undefined.

Newton was the first who used positive, negative, integer, and fractional exponents. Clearly, 0 0 is one of those expressions that do not have a definitive meaning but can be given a “contextual” one. Therefore, the value of 0 0 depends on the context where it occurs; you might wish to substitute it with 1, indeterminate, or undefined.

The context in which 0 0 is taken to be 1 is, e. This in turn maintains the beauty of the Pascal Triangular numbers. It is too important to be arbitrarily restricted! By contrast, the function 0 n is quite unimportant. There must be a conviction that mathematics teacher and researchers in mathematics education have much to learn from each other, especially at a time when the school and adult curricula are converging.

Based on my experience, I offer the following three distinct headings:. Unfortunately, mathematics has been fundamentally depersonalized to “something machines do” and that the meaningful response is that we need always to emphasis that mathematics has little value divorced from imagination. Machines will always do ‘imaginationless’ mathematics better than humans. But “mathematics imagination meld” is needed by society and it can become a fascinating subject for most children in the classroom.

Too many pupils now think that mathematics is boring. Mathematics can and must be made more fun, more relevant, and more challenging, for pupils and for teachers. The use of Internet interactive technology in the classroom can add a new and precious variety. This variety can help to engage and hold pupils’ attention, and can raise the chances that the lesson will have been judged a success.

The new interactive technology can help to attract and retain teachers by making the whole process more business-like, more efficient and more effective. However the provision of appropriate hardware, software and training remain expensive and intractable hindrances to progress. There is a “math” video series [Harlan Meyer, Diamond Entertainment, ]. One is called Addition, then Subtraction, Multiplication and, of course, Division. The division segment of the series starts by misspelling the word quotient.

Then the “star” of the video shows how to divide by using repeated subtraction; however, she asks “If I have 12 doggy bones and I take away 4 groups of 3 bones, how many will I have left? Unfortunately, there are many instances like this which sent your blood pressure through the roof. Zero is nothing. So just remember nothing INTO something is nothing. Teaching kids to count is fine, but teaching them what counts is best.

One may view “division” as a subtraction operation. That is why division is the “inverse” operation for multiplication, which is an addition. So dividing by “0”, has no meaning, because the question: how many times you can subtract nothing from something? The question itself makes no sense. The act of dividing by zero is meaningless. Therefore, it does not make to ask further what is its result, whether it is indeterminate or not?

Zero is an important concept, so time should be spent establishing that from early age one has some understanding of zero; zero, nought, nothing – as ever, the language should be varied.

In absence of a concept of zero there could have been only positive numerals in computation, the inclusion of zero in mathematics opened up a new dimension of negative numerals. Zero, when used as a counting number such as zero defect , means that no such objects are present. A concept and symbol that connotes nullity represents a qualitative advancement of the human capacity of abstraction. As always, concepts are only real in their correct context.

In other words, the distribution takes place across an equal sign among the number specified in the denominator on the left hand side. Since he specifies zero people in the distribution, the transaction is not taken place.

The result of interest is on the right-hand side. It is certainly true that if you do not distribute the pie, you retain it; but when you use an equal sign, you do imply the result of some real transaction to the other side.

This is certainly true for apple pies. The results may differ with other varieties of pies, not all of which have been reviewed! Once you understand what division is , then there should be little difficulty in understanding why division by zero is not allowed. There could be many interpretations for this definition, but there is no reason. As you demonstrated many times, allowing division by zero causes contradiction, thereby making that mathematical system useless.

On the other hand, prohibiting division by zero has not yet known to cause any contradiction. If any, that’s the only reason why we define division as it currently is. Division by zero does cause contradiction. That’s why we can not divide 2 apples among zero people. It’s meaningless, and has no other “interpretations”. The act of “distributing” apples cannot be performed.

However, adding zero apples to 2 apples we get 2 apples. Notice that, in addition and subtraction operations we must have the same “dimensions”, i. However, in division operation, this is not a necessary condition, such as in speed, expressed, e.

It might even have a hybrid dimensionality, like momentum in physics. But I don’t think anyone in his right mind considers this. It could have been a hundred times worse than this and I will not lift a finger against it.

But, what I’m combating is the act of dividing by zero in the first place, the carelessness of our educators, and not willing to know that they are misleading students. Do you know of any? Whenever, mathematics is distorted and sensationalized, or even pseudo-mathematics is used uncritically, a disservice is done to public understanding of mathematical fact.

What I am attempting to signify here is nothing more than this: in applied mathematics dividing by zero is a meaningless operation. It may also make you wonder that the word “cifra” in Russian means “written numbers. Zero in German is called ‘Null’. French use “zero” as in English. However “chiffre” is the equivalent of the German “Ziffer”, a single digit numbers integers from 0 to 9.

Number s are called “nombre s “. The ancient Egyptians never used a zero symbol in writing their numerals. Therefore there was no function for a zero in writing their numerals. The two applications of the zero concept used by ancient Egyptian scribes were: 1 as a zero reference point for a system of integers used on construction guidelines, and 2 as a value that resulted from subtracting a number from an equal number. It is quite extraordinary that neither the Egyptians nor the Greek were able to create a symbol to represent zero, or nothingness.

The conceptual difficulty may have been that the zero is something that must be there in order to say that nothing is there. The Hindu-Arabic numerals were used for written calculations in the West not before the twelfth century, when Arabic texts were translated into Latin. Babylonians also used a zero, approximately at the same time as Egyptians, before BC. Certainly, zero’s application in our base 10 decimal system was a step forward, as logarithms of Napier and others brought into use. Notice that by this fallacy one tries to define “infinity” in terms of zero.

Unfortunately, similar practices seem to prevail to the present day. A similar fallacy exists for logarithms of zero which is believed by many to be negative infinity. A reader from Canada kindly sent me an email with the subject heading: “Two-dollar bills don’t exist”.

Here’s a little bit of tongue-in-cheek math! How many dimes are in a quarter? How many two-dollar bills are in a five-dollar bill? In Canada, you are right on the money! In US we do not have such a dilemma! Mathematics is a human endeavor which has spanned over four thousand years; it is part of our cultural heritage; it is a very useful, beautiful and prosperous subject. Mathematics is one of the oldest of sciences; it is also one of the most active; for its strength is the vigor of perpetual youth.

Mathematics is also our native language. Numbers are a cultural phenomena, humans invented them to quantify the external world around them. The external world is qualitative in its nature. However, human can understand, compare and manipulate numbers only. Therefore, we use some measurable and numerical scales to quantify the world.

This enables us to understand the world by, for example finding any relationship, manipulating, comparing, calculating, etc. That is, to make an Analytical Structured Model for the external world. Then we use the same scale to qualify it back to the world. If you cannot measure it, you cannot manage it. This is the essence of human’s understanding and decision making process. The Origin of Algebra: The Vedic Mathematics that is enjoying a vogue in mathematics pedagogy these days is the pre-modern Indian mathematics preserved in Sanskrit; in this category there are a number of mathematical methods many of which were adopted by Muslim recipients and became the basis of our algebra in 13 th century.

The early use of the Arabic word “al-jabr” was in the sense of “the resetting of bones,” and this term was adopted by the early Muslim algebraists as an analogy for what we today call “combining like terms. Again, The word “algebra” comes from a phrase in bold below in the title of an Arab book ” Kitab al muhtasar fi hisab al gabr w’al muqubalah.

The book covered simple equations like the one in the preceding section, also quadratic ones involving x 2 , as well as other areas such as geometry and the division of inheritances.

The “House of Wisdom” was involved in Al Ma’mun’s expedition to measure the size of the Earth, which Al-Khorezmi afterwards estimated to have a circumference of Arab miles. We are not sure how big the Arab mile was, the actual figure is about of our miles. Al-Khorezmi came from the oasis of Khorazem, at the northeast of Persia. He is also credited with helping establish among the Arabs the Indian numbering system, using decimal notation and the zero.

Previous systems of writing numbers used letters, like the Roman numeral systems or the cruder ones of the Greeks and Hebrews. When Al-Khorezmi’s book on the new system reached Europe, the Europeans called its use “algorism” or “algorithm,” a corruption of the author’s name.

Today “algorithm” means method of calculation, and the rise of computers has led to extensive work on developing efficient computer algorithms The word algebra originated from the title of the book “ilm al-jabr w’almuqabala”, written during the 9 th century by a Persian Muslim mathematician named al-Khworizimi who wrote in Arabic which was the language of scientific era of the Islamic world.

Therefore, the word Algebra derived from the Arabic word Al-jabr meaning combining the like terms. Finally I would like to quote Johann Carl Friedrich Gauss saying “Mathematics is the queen of the sciences and number theory is the queen of mathematics. When these scholarly treatises were being translated by European accountants, they translated 1, 2, 3, The scribe asked what to write and was instructed to draw an empty hole, thus introducing the present notation for zero.

Hindu and early Muslim mathematicians were using a heavy dot to mark zero’s place in calculations. Perhaps we would not be tempted to divide by zero if we also express the zero as a dot rather that the 0 character. You might ask then how did the Romans do calculations with their numerals notations? Romans typically relied on the Chinese abacus , their version of our modern calculator, visit, e.

By using pebbles as counters, there was no need to use Roman numerals. People known as “calculatores” after “calcule”, Latin for “pebbles” , did the math used to tally totals in addition, subtraction, division and multiplication. For us using Roman numerals system to perform arithmetic operations such as division, or multiplication are very difficult if not impossible. In modern days they are used for decorative purposes only. Zero as a concept, was derived, perhaps from the concept of a void.

The concept of void existed in Hindu philosophy and the Buddhist concept of Nirvana, that is: attaining salvation by merging into the void of eternity. As pointed out by George Wilhelm Friedrich Hegel , “India, such a vast country, has no documented history. The Arabic writing mathematicians not only developed decimal notation, they also gave irrational numbers, such as square root of 2, equal rights in the realm of Number. And they developed the language, though not yet the notation, of algebra.

One of the influential persons in both areas was Omar Khayyam , known in the west more as a poet. I consider that an important point; too many people still believe that mathematicians have to be dry and uninteresting. Initially, there was some resistance to accepting this significant modification to the time-honored Roman numerical notation, in particular from the privileged job-secured Roman numerical calculation experts: The Tax Gatherers:.

Among the trite objections to leaving Roman numerals for the new notation was the difficulty in distinguishing between the numeral 1 and 7.

The solution, still employed in Europe, was to use a cross-hatch to distinguish the numeral 7. The introduction of the new system indisputably marked the democratization of mathematical computation by its simplicity and lack of mystery.

Up to then the “abacus” was the champion. Abacus was a favorite tool for a few and praised by Socrates. The Greek’s emphasis on geometry i. They simply had no use for zero. Greeks were not too much interested in arithmetic, believing in inherited nobility of a few, the Greeks had the adage “that arithmetic should be taught in democracies, for it teaches relations of equality, but that geometry alone should be reserved for oligarchies, as it demonstrates the proportions within inequality. Sacrilegious as it may sound on first impression, the notation of zero is at heart nothing more than a directional separator as in the case of a thermometer.

It is, in actuality, “not there. The digit 0 serves this purpose. Zero became a part of the Natural Numbers System in the last century when Giuseppe Peano puts it in his first of five axioms for his number theory.

One may think of an analogy. Zero is similar to the “color” black, which is not a color at all. It is the absence of color, while the Sun Light contains all the colors. When we write 10, we mean 1 ten and 0 ones. In some number systems, it would be redundant to mention the 0 ones, because zero means there are no objects there. Place value uses relative positions. The usage of zero here is more of a qualitative than quantitative. Therefore, it is called an operational zero.

You are right in that one can express any number in different base systems that exclude zero. However performing any arithmetic operations becomes very tedious, as it is evident, for example with Roman numerical system. That is the main historical reason for the success of decimal numerical system in initiating scientific discoveries, and faster, easier for everyone, and provides more accurate commercial transactions.

Here, my dear reader has mixed the two distinct notions of zero: Zero as a number being used in our numerical systems AND as a concept for ‘nothing’. As a result of this mixed-up, he is “wondering” at his own mental creature. We used to think that if we know one, we know the other.

We are finding out that we must learn a great deal more about “AND”. Natural numbers are positive integer numbers. One horse, two trees, etc. However, the arrival of zero caused the inevitable rise of the even more nefarious numbers: The negative numbers. What about negative numbers? The negative sign is an extension of the number system used to indicate directionality. Zero must be distinguished from nothing.

Zero belongs to the integer set of numbers. Zero is neither positive nor negative but psychologically it is negative. The concept of zero represents “something” that is “not there,” while zero as a number represents the lowest of all non-negative numbers. In High school Algebra books they like to teach about numbers.

You know whole numbers, natural numbers, rational numbers, irrational numbers, and integers to name a few. The problem that I often run across is where does the zero fit in. For instance ‘a positive integer’, does this include zero?

We know that whole numbers include 0, but it is a positive whole number. Can you clarify some of this for me? Why or why not they are included or excluded. I really wish they would put a little more information into these books as your web sight shows we need it. So I want to thank you, for bringing things into the light.. You are right, unfortunately some algebra books are confusing on categorizing zero in our numerical systems.

However, the accepted and widely use categories for inclusion of zero as a positive number is “non-negative integers”, while for excluding it from positive integer the terminology “positive integers” is used. Similarly, for the real numbers involving zero, the following four categories: “positive”, “negative”, “non-negative” and “non-positive” are being used. The last two categories include zero, while the first two exclude zero, respectively.

Therefore, as you see, the first two sets are the subsets of the last two, respectively. I’ve been teaching math for four years but it is only this year that I encountered this problem. I always thought and believed that zero is neither positive nor negative. It’s only when we used the book International Student 7 th Ed. This is rather confusing to me and to my students because I told them that zero is neither positive nor negative, then why did these authors attach a negative sign on zero?

Can you please help me on this one? What could probably be their reason for writing these? These actually confused my students and even me myself in the process. I agree with you that it is confusing.

It is also a difficult and uncomfortable situation when you as a knowledgeable teacher want to correct the textbook, and your students taking the textbook as the ultimate authority as if it’s a Bible. You might like to remind them by mentioning that the purpose of education is critical thinking for oneself. You are right also in that: The additive inverse of any number is a unique number.

Therefore, the additive inverse of 0 cannot be ” -0, or 0″. Thanks goodness! Moreover, the additive inverse of zero is itself. This property of zero also characterizes the zero i.

Furthermore, zero is the Null element for addition. Any operation has a unique Null. The inverse of a Null element for any operation is itself. For example, the Null element for both multiplication and division operations is 1. Most modern textbooks apply concepts such as “even” only to “natural numbers,” in connection with primes and factoring. By “natural numbers” they mean positive integers, not including zero.

Those who work in foundations of mathematics, though, consider zero a natural number, and for them the integers are whole numbers. From that point of view, the question whether zero is even just does not arise, except by extension. One may say that zero is neither even nor odd. Because you can pick an even number and divide it in groups, take, e.

But can you divide zero? That’s why there are so many “questions. If you feel that the question if zero is an even number is of no practical value at all, let me quote the following news from the German television news program ZDF “Heute” on Oct. Smog alarm in Paris: Only cars with an odd terminating number on the license plate are admitted for driving.

Cars with an even digit terminating were not allowed to be driven. There were problems: Is the terminating number 0 an even number? Drivers with such numbers were not fined, because the police did not know the answer.

Similar phenomenon occurred recently November in New York city when the governor’s decided to allow cars with even numbers and zero at the end of their number plates to fill up at gas stations on even days the Sandy strong hurricane.

It came to the attention of a BBC reporter. I suggest a convention, i. I offer two arguments:. A1: “Odd” numbers are spaced two apart. So are “even” numbers. Proceeding downward, 8,6,4,2,0,-2, While odd numbers 9,7,5,3,1,-1, A2: Let two softball teams play a game, with each player betting one dollar a run to the opposing team.

Further presume that no runs are scored due to beer consumption and no extra innings are allowed because it got dark. The final score is zero to zero. If a player is asked by his wife whether he won or lost, he would probably indicate that he “broke even”. As the old math teacher said: ” Proof? Why any fool can see that. In some parts of the world, the phrasing “naught” and “aught” are used but it is quite uncommon to hear “zero. However, in the US Army there is an additional curious habit of saying “duece” instead of “two”.

President before the end of their term in office, if they were elected in a year that ended with 0. The first victim of the curse was William Henry Harrison, whose troops killed the Indian chief in the zero factor has one exception, i. The term “zeroing in on whatever ” might have originated also with the military. The “zero” in this term might refer to the distance from the last bomb dropped or the last shell fired to some target.

The aim is always to try in reducing this distance to zero. On a roulette wheel , there is the number Zero which is neither Red nor Black. It is considered neither Even nor Odd. Ernie : I’ve put a number of cookies in that Jar. You can have them if you give me your teddy.

It is not uncommon these days to hear, on dating scene, the phrase “get rid of the ‘zero’ and get yourself a hero”. Zero is often used in the description of an undesirable individual as illustrated in following cartoon:. Today zero has a meaning not just of a number, but as the bottom, or failure.

He made no baskets, or, he made zero baskets — meaning he failed to score. Or he gave zero assistance. If you are familiar with numerology, you notice that there is no zero to work with in the numbers that correlate with the alphabet, strange?

Not at all. The absence of zero may suggest that the Pythagorean who first developed the duality between numbers and letters were not aware of the zero notion. The notion of zero is much younger. In tennis scores, zero is called “love,” because zero looks like an egg, the French called it “l’oeuf,” which is French for “egg.

Back in medieval times, tennis’s four points were 15, 30, 45 later abbreviated to 40 , and 60, or game. On the telephone keypad, zero has the honor of representing the operator. There is no zero in most games, such as plying cards after all who wants to win zero! Zero is placed at the end of the keypad on the computer and at the bottom of the keypad on the telephone.

Is zero the beginning or the end? Notice that on a calculator’s keypad the numbers starts with the largest numbers on the top and work their way down to zero. What about the o and 0 being right next to each other on the PC keyboard? Numbers are located three places. First it is located on the keyboard keys with the range 1, 2, Second, on the right of the keyboard is a calculator-like pad where zero is the last listed number.

Finally, there is a list of functions key, however there is no F0 because that could translate into no function and what would be the point of having a key “without” function. There will always be questions about the true meaning and function of zero.

Is it the end or the beginning? What does ground zero mean? Some use it as starting point; the military uses it as an ending point. The resistance against zero can be noted even at the architectural level in buildings where the ground-level is rarely denoted as the zeroth-level as it should be.

However, for mathematicians it comes easily to label the floors of a building to include zero, for example, the Department of Mathematics’ building at the University of Zagreb in Croatia has floors numbered as -1, 0, 1, 2, and 3. In fact, this is not a particularity of one building but a common practice in modern buildings in large cities such as Buenos Aires.

In most European countries the floors are always numbered starting from 0. We do have a special word to say ‘ground floor’ in a conversation, not using 0, but the elevators will always offer you a “0 button” for the ground floor.

Now is the time to test yourself. By now you should know the answer and the why. For example, for Part C: Any number divided by itself is 1. Well, if we allow this you end up with some inconsistent results. One may say that “I understand why it’s considered meaningless to divide a number by 0. But why is the answer considered meaningless when dividing 0 by 0?

This is possible because anything multiplied by zero equals zero. One should never divide by zero. Division by zero is a meaningless operation. How could you divide 3 apples among zero people!

How could you divide “nothing” among nobody! This is equal to any number because when you multiply any number by zero, you get zero. The ancients Greek had no applied mathematics. The practical and useful mathematics as they had, was developed prior to, independent of and unsupported by any theoretical structure.

Moreover, far from supporting useful mathematics, the theoretical systems tended to inhibit its development mainly because they denouncing the treatment of one as a number.

This situation persisted through the middle ages and beyond. You may say that any number, like 1 for example, is simply a “unit” for counting. For example the question, “what do you think of when you think of the number 26? They think of 26 as a number, while others think of 26 as a “unit” for counting. The Newtonian concept of number which; defines number as the ratio of a magnitude to a unit magnitude of the same kind.

The main objection is that the notion of magnitude itself has never been properly defined, and this definition fails in the particular case of complex numbers. Presumably this is because there are no complex magnitudes to provide the necessary ratio.

We are interested in a more objective answer to the question, “is 1 a number or just a ‘unit’ for counting? Interestingly enough, some teachers make the statement “I do not think that numbers exist because a number does not refer to anything physical. One must be aware of the facts that when we use a number it may not have any “dimension” at all.

For example, probability is dimensionless. It is a number between zero and one expressing the degree of your belief in occurrence of an event, not any quantity. However, the relative error of the measurement is dimensionless, that is a pure number without any units. Fermat’s Last Theorem FLT is another example that illustrates the ability to separate numbers and quantities.

This can be applied to a quantity as follows– there are no cube whole number pairs that add to a cube. But what about the fifth dimension? And the sixth? The only logical explanation is that numbers do not need to refer to physical objects, numbers exist perfectly well on their own.

The illustrative examples given in this Section are particularly vivid because they allow you to demonstrate the separation of numbers and quantities to your students at early age. Why is 1 the number one not considered prime?

I don’t consider it a prime for my own reasons, but would like to hear somebody else’s views. If I define a prime as a positive integer, divisible only by itself and one; then the number 1 is “special”. Thus, a prime has Two constraints: A: Indivisibility by any number other than itself, and B: the trivial Exception of One.

A prime number has exactly and only two factors: one and the number. However a composite number has more than two factors. Finally, one is neither prime nor composite because it has only one factor. The question, whether 1 is prime or not goes back to Socrates. The difficulty they had was not considering 1 as a number but a Unit measuring other numbers. In India, when writing about large number, they use Laky. Lash is Sanskrit meaning The word appeared first, in non-mathematical works in epic and dharmasastra literature.

The word “lacquer” Lack in German stems from this word, since huge numbers of “lacquer” lice sit on the “lacquer” tree producing what is now called “lacquer”. The word came into scientific use through the early Muslim mathematicians into Medieval Latin and from there into all the European languages. The concept of infinity in mathematical systems is expressed by the sign.

As far as history is concerned, the most common similar medieval symbol is the snake biting its own tail. It is as if represents a double endlessness or eternity. He also wrote in the Philosophical Transactions that “Infinitely means more than any Finite number assignable”.

Later, the infinite numbers have been discussed in a formal way by George Cantor in Cantor went to some effort to make connections with ancient and medieval ideas about infinity in his famous series of papers on set theory. Aristotle considered the infinite as something for which there is no exit in an attempt to pass through it. In his Physics: Book III , he wrote “It is plain, too, that the infinite cannot be an actual thing and a substance and principle.

To facilitate a visual understanding of the infinity concept, you may wish to use the following demonstration for your students: Draw to straight line segments parallel to each other on the board.

Make one line segments clearly longer say, twice length than the other line segment, as shown in the following graph:. You may also like to pose a questions such as, What do you get when you add up infinitely many positive numbers? What do you think the following adds up to? You may also give a verbal explanation. Suppose you are given a piece of wood of length 1 meter. Cut it into to halves, put aside one half and then cut the other half into two halves again.

Repeat this cutting process for eternity. Now, put all the pieces together, what do you get! Unfortunately, there are teachers who continue misleading students as the following argument illustrates:.

But when you start subtracting zeroes, even infinite times, you never get down to zero! The notion of zero brings another wearying and yet intriguing questions: Is our current century the 20 th century or the 21 st century? Does that mean the millennium actually started in ?

As you may know, our calendar was improperly set up by a monk in about AD. Since the zero’s concept was not available yet, he began the calendar with year 1. Anno domini means “in the year of our lord”; but by starting at 1, the calendar does not correctly reflect the verbal statement. As year one begins, Christ is just born. As year two begins Christ is one year old.

The second Century begins with and the second millennium begins with Still there is a confusion when referring to any particular year in any century. For example, the American Independent achieved in 18 th century, but we refer to it as , “as if” it occurred in duting 17 th century. Ordinal numbers, which the Gregorian calendar uses, indicate sequence.

Thus “A. Think of a carpenter’s ruler, if you will; the first inch is the interval between the edge and the one-inch mark. Thus, e. Cardinal numbers, which astronomers use in their calculations, indicate quantity. Zero is a cardinal number and indicates a value; it does not name an interval. Thus “zero” indicates the division between B. Continuing with our example, put two rulers end to end: although there is a zero point, there is no “zero’th” inch.

As it stands now, we refer to years with ordinal numbers and to ages with cardinal numbers. Thus a child less than a year old is usually said to be so many weeks or months old, rather than “zero years old.

That is to say, the last twelve months before the birth of Christ and the first twelve months after the birth of Christ would be the years 0 B. For more on this, you may like also to visit the Web site Zero.

This is quite revealing of the cultural predilections of the time when the calendar was reorganized, first under the Julian scheme undertaken under the auspices of the Roman Emperor, Julius Caesar, after whom the month of July was named, and subsequently under the Gregorian calendar currently in use, which was devised during the reign of Pope Gregory. What is quietly yet magnificently revealed by this now-curious omission is the absence of the notion of zero in the numbering systems then in use.

When the notion of zero was subsequently introduced in the west in the Middle Ages, it could hardly have been regarded as feasible to rewrite the entire calendar, if the debate occurred in the first place. Clearly then, our ideas about numbers permeate our culture.

A visitor of this site asked me “I want to know what the opposite of zero is. The concept of opposite is a human invention in order to make the world manageable, there is no real opposite in nature. Is day opposite of night?

 
 

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