# why was I not told 1/0 = infinity **URL:** \ **Category:** Factual Questions\ **Created:** [January 16, 2004, 6:11pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804 "2004-01-16T18:11:40Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![shea241](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@shea241](https://boards.straightdope.com/u/shea241)\ **Post date:** [January 16, 2004, 6:11pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/1 "2004-01-16T18:11:40Z")
going through school I was always taught that if a number was divided by 0 then it was not defined. Or not probable. Why is it that high school and below teaches you that you can’t do this. That is you can’t divide any number by 0. Of course you can and the answer is infinity ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [January 16, 2004, 6:15pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/2 "2004-01-16T18:15:59Z")
It’s true that the answer cannot be _nunmerically_ defined. Infinity is not a number, it is a concept. Therefore “1/0 = infinity” is a philosophical statement, not a mathematical one. ---
**Author:** ![Kent\_Clark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kent_clark/32/105_2.png) [@Kent\_Clark](https://boards.straightdope.com/u/Kent_Clark)\ **Post date:** [January 16, 2004, 6:32pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/3 "2004-01-16T18:32:33Z")
I was taught that 0 had no value, i.e. no units, and therefore the concept of dividing something by 0 was meaningless. In other words, divide that cake into 0 pieces. It’s a meaningless statement. ---
**Author:** ![SCSimmons](https://avatars.discourse-cdn.com/v4/letter/s/e495f1/32.png) [@SCSimmons](https://boards.straightdope.com/u/SCSimmons)\ **Post date:** [January 16, 2004, 6:46pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/4 "2004-01-16T18:46:43Z")
> [@shea241](#): > > going through school I was always taught that if a number was divided by 0 then it was not defined. Or not probable. Why is it that high school and below teaches you that you can’t do this. That is you can’t divide any number by 0. Of course you can and the answer is infinity No, it’s not. “a divided by b = c” means that b times c = a. So, “1 divided by 0 = infinity” means that 0 times infinity = 1. The meaning of _that_ mathematical phrase is that the partial sums as n increases without limit of n zeroes (0+0+0+0 …) is one. And this is not the case-no matter how many zeroes you add together, the sum is still zero. ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [January 16, 2004, 6:49pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/5 "2004-01-16T18:49:05Z")
Who told you that 1/0 = infinity? The teachers who told you it was undefined in high school were right. In special cases it can make some sense to say 1/0 = inf as a shorthand, but it is a literally incorrect statement. Most often it is something like taking a limit (and saying ‘the limit is infinity’ is another shorthand, since it treats infinity like a number). If an instructor was using it, they are expecting you to understand the assumptions and circumstances they’re working with. If they are a good instructor, they’ll probably explain exactly what they mean to you (maybe not in the middle of class however). There’s been threads about this before with more and better explanation than what I’m saying here, but I don’t know if search is working (I’m afraid to try). ---
**Author:** ![HPL](https://avatars.discourse-cdn.com/v4/letter/h/3da27b/32.png) [@HPL](https://boards.straightdope.com/u/HPL)\ **Post date:** [January 16, 2004, 6:59pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/6 "2004-01-16T18:59:29Z")
> [@shea241](#): > > going through school I was always taught that if a number was divided by 0 then it was not defined. Or not probable. Why is it that high school and below teaches you that you can’t do this. That is you can’t divide any number by 0. Of course you can and the answer is infinity Not sure what you mean by High School. I’m in College Calculus and just yesterday the instructor was talking about how you can’t divide by Zero because it’s undefined. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 16, 2004, 7:03pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/7 "2004-01-16T19:03:56Z")
Mathematically speaking, “infinity” is a meaningless word. In a specific context, “infinity” does mean something, but that varies depending on what words are around it. Division by 0 is undefined for the reasons that **SCSimmons** mentioned. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [January 16, 2004, 7:16pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/8 "2004-01-16T19:16:51Z")
Besides, think about how you check division. If you take 6 / 3 = 2, you’d check it using 2 x 3 = 6, right? But even if inf has a value (which it doesn’t), does inf x 0 = 1? No, it does not. ---
**Author:** ![ParentalAdvisory](https://avatars.discourse-cdn.com/v4/letter/p/53a042/32.png) [@ParentalAdvisory](https://boards.straightdope.com/u/ParentalAdvisory)\ **Post date:** [January 16, 2004, 7:26pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/9 "2004-01-16T19:26:06Z")
My Windows Calculator says, “Cannot divide by zero.” So basically, the “1/0 = infinity” is as equal to “1/0 = Santa Clause” ---
**Author:** ![GargoyleWB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gargoylewb/32/199_2.png) [@GargoyleWB](https://boards.straightdope.com/u/GargoyleWB)\ **Post date:** [January 16, 2004, 7:34pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/10 "2004-01-16T19:34:33Z")
One poster mentioned limits, which when studying those (calculus and on), it is helpful to think of the 1/0 case as being infinity, even if that isn’t pedantically true. For example, when talking of an asymptote of the function y=1/(x-1), as the denominator approaches zero, the function shoots up to infinity. Think of 1/0 as being 1/(1-0.9999999…) to see what I mean. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 16, 2004, 7:44pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/11 "2004-01-16T19:44:27Z")
> [@GargoyleWB](#): > > One poster mentioned limits, which when studying those (calculus and on), it is helpful to think of the 1/0 case as being infinity, even if that isn’t pedantically true. For example, when talking of an asymptote of the function y=1/(x-1), as the denominator approaches zero, the function shoots up to infinity. Only as you approach from the right. As you approach from the left, the function decreases without bound. ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [January 16, 2004, 8:08pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/12 "2004-01-16T20:08:38Z")
The way I would describe it is that we normally deal with real numbers (0,1,pi,-root(2),10^19,etc). Here division by zero is undefined. Sometimes we do something for which the concept of infinity (of some sort - different concepts can be labelled ‘infinity’) is useful (eg. umm… someone help me with an easy example? complex analysis?), and we define numbers to include it. However, this has drawbacks of its own; for instance reak numbers have many nice properties such as x + y \> x if x \> 0, etc, which fail if we do. So depending, we use a different set of numbers. _However_, often we’re sloppy, and since it’s obvious, or doesn’t matter, which type of numbers we’re using, we just let everything be implicit. For instance, 3+4 is almost always 7, so you don’t have to specify. Or -\>inf is mathematical shorthand for ‘increases arbitrarily’, and it can be helpful to think of this as ‘getting close to inf’ but that’s not what it is really. As an analogy, what would you say if I asked you what temperature is 10[sup]o[/sup] below zero? Probably -10[sup]o[/sup] as that’s the answer in c and F. But then I say “AHA! I was using Kelvin! You’re wrong, there is no answer.” ---
**Author:** ![BJMoose](https://avatars.discourse-cdn.com/v4/letter/b/5fc32e/32.png) [@BJMoose](https://boards.straightdope.com/u/BJMoose)\ **Post date:** [January 16, 2004, 8:24pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/13 "2004-01-16T20:24:00Z")
Oh good Lord! - have I created the Internet equivalent of an urban legend? Last summer in [one of the threads](http://boards.straightdope.com/sdmb/showthread.php?t=198042) generated by Cecil’s column on whether 0.999~ = 1, I kicked around the theoretical idea that 1/0=infinity (cf. post #13 in that thread). Hadn’t heard the notion anywhere; it occured to me while pondering my assertion that a vertical line on a Cartesian graph could be said to have “infinite slope”. I’m not a mathematician, don’t play one on TV, and never got past College Algebra at Wossamotta U. Seriously, it wouldn’t surprise me if this notion has occured to others. But it _is_ awful self-flattering to think that an idea one has had has gained some currency. In any case, **SCSimmons** ’ example pretty much demolishes the notion. I’m not saying anything beyond that because I’ve learned the hard way that arguing with mathematicians is no fun at all. 😉 [by the way - **panamajack** is right to doubt this Board’s ability to do a search while the hamsters learn the new software; two different searches for the thread linked above came up dry - had to find it the hard way] ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [January 16, 2004, 9:14pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/14 "2004-01-16T21:14:06Z")
BJMoose, believe me, I think other people have thought of it before. It _is_ a good idea, though, that’s why it’s so attractive. The problem isn’t that people come up with ideas like this - they can be valuble - it’s people who can’t accept it if they don’t work. ---
**Author:** ![shea241](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@shea241](https://boards.straightdope.com/u/shea241)\ **Post date:** [January 16, 2004, 10:56pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/15 "2004-01-16T22:56:25Z")
I don’t want to argue to death my idea but for those of you who wanted to know it kind of came to me when I was looking at an equation for limits where the limit was D.N.E because 0 was in the denomenator. Then I looked at it from a number line point of view for example 1/1=1 1/.1=10 1/.000001 = 1000000 and so on so to me it made sense that as the denomenator approached 0 the result became bigger and when it reached 0 the result would be infinite. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 16, 2004, 10:58pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/16 "2004-01-16T22:58:00Z")
> [@shea241](#): > > I don’t want to argue to death my idea but for those of you who wanted to know it kind of came to me when I was looking at an equation for limits where the limit was D.N.E because 0 was in the denomenator. Then I looked at it from a number line point of view for example 1/1=1 1/.1=10 1/.000001 = 1000000 and so on so to me it made sense that as the denomenator approached 0 the result became bigger and when it reached 0 the result would be infinite. What happens as you plug in small negative values? ---
**Author:** ![shea241](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@shea241](https://boards.straightdope.com/u/shea241)\ **Post date:** [January 16, 2004, 11:03pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/17 "2004-01-16T23:03:06Z")
I already thought about that and I was thinking that it would be -infinity. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 16, 2004, 11:05pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/18 "2004-01-16T23:05:14Z")
> [@shea241](#): > > I already thought about that and I was thinking that it would be -infinity. So by the same argument, you can conclude that 1/0 = infinity and that 1/0 = -infinity. Not a very good argument, don’t you think? ---
**Author:** ![shea241](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@shea241](https://boards.straightdope.com/u/shea241)\ **Post date:** [January 16, 2004, 11:12pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/19 "2004-01-16T23:12:11Z")
no what I’m saying is 1/0=inf and -1/0=-inf also for the rule about 1/0=inf so inf \* 0=1 wouldn’t necessarily be fair to say its right when talking about numbers like inf and 0. thats like the rule x/x = 1 so whats 0/0=??? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 16, 2004, 11:15pm UTC](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804/20 "2004-01-16T23:15:33Z")
> [@shea241](#): > > no what I’m saying is 1/0=inf and -1/0=-inf also for the rule about 1/0=inf so inf \* 0=1 wouldn’t necessarily be fair to say its right when talking about numbers like inf and 0. thats like the rule x/x = 1 so whats 0/0=??? As you approach 0 from the right, 1/x increases without bound. As you approach 0 from the left, 1/x decreases without bound. Which should be the value of 1/0? x/x is undefined when x = 0. [Next page](https://boards.straightdope.com/t/why-was-i-not-told-1-0-infinity/224804.md?page=2)