# Is "1" an odd number? Is "2" even? **URL:** \ **Category:** Factual Questions\ **Created:** [October 9, 2007, 2:16am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023 "2007-10-09T02:16:24Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Parthol](https://avatars.discourse-cdn.com/v4/letter/p/dec6dc/32.png) [@Parthol](https://boards.straightdope.com/u/Parthol)\ **Post date:** [October 9, 2007, 2:16am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/1 "2007-10-09T02:16:24Z")
I must be crazy. I have this memory from highschool math classes that while most positive integers are even or odd, the numbers 0-2 were classified as neither, but were instead called “unique” numbers. (I’m more certain I learned this for 0 and 1; less so for 2.) Sadly, my Google-fu turns up nothing to support my recollection, and [this](http://en.wikipedia.org/wiki/Even_and_odd_numbers) wikipedia link seems to actively dispute it. Does the notion of these numbers being unique, rather than even or odd, have any validity? Is this something that used to be taught but is no longer? Or am I merely suffering from a case of faulty memory? Thanks! -P ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [October 9, 2007, 2:28am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/2 "2007-10-09T02:28:02Z")
The only thing unique is that 0 is the identity value for addition, 1 is the identity value for multiplication, and 2 is the only even prime number. Maybe it’s little factoids like that you’re recalling? ---
**Author:** ![papaw](https://avatars.discourse-cdn.com/v4/letter/p/b77776/32.png) [@papaw](https://boards.straightdope.com/u/papaw)\ **Post date:** [October 9, 2007, 2:28am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/3 "2007-10-09T02:28:31Z")
IANAM(athemetician) , but I can’t see how 1 and 2 are not considered respectively odd and even, given that in my mind, at least, even means divisible by 2. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [October 9, 2007, 2:29am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/4 "2007-10-09T02:29:37Z")
I don’t remember ever being taught that. 1 was odd; 2 was even. 0 is more problematical, as it has many unique properties, but not having it be even would create problems of its own. The one exception I can think of is the elementary definition of an odd number - a number that leaves a remainder of 1 when divided by 2 - which obviously would leave 1 out. However, that is not a good definition of odd number. Try [these](http://www.google.com/search?sourceid=navclient&ie=UTF-8&rls=GGLD,GGLD:2005-18,GGLD:en&q=define%3a+odd+number): > [@](#): > > A whole number that cannot be evenly divided by 2. > [http://classic.sidwell.edu/academics/lower\_school/LS\_Math\_Adventures/glossary.htm](http://classic.sidwell.edu/academics/lower_school/LS_Math_Adventures/glossary.htm) > > An integer that is not a multiple of 2. The odd numbers are { . . . , –3, –1, 1, 3, 5, . . . } > [Maths Dictionary | Simple Maths | Sums Simple is key stage maths made easy](http://www.sumssimple.com/maths-dictionary.html) And if you use this definition, even the divide by 2 rule is accommodated: > [@](#): > > A number that when divided by two gives a remainder of positive or negative 1. Examples are 1, 3, 5, 7 and 9. It is represented by a number that has 1,3,5,7, or 9 in the ones position. > [www.numbernut.com/glossary/o.shtml](http://www.numbernut.com/glossary/o.shtml) There is no question at all that 2 must be even, though. And check the definition of [even number](http://www.google.com/search?num=50&hl=en&newwindow=1&safe=off&rls=GGLD%2CGGLD%3A2005-18%2CGGLD%3Aen&q=define%3A+even+number): > [@](#): > > An integer (positive whole numbers, zero, and negative whole numbers) divisible by 2 (with no remainder). … > [www.cliffsnotes.com/WileyCDA/Section/id-106327.html](http://www.cliffsnotes.com/WileyCDA/Section/id-106327.html) > > An integer that is a multiple of 2. The even numbers are { . . . , –4, –2, 0, 2, 4, 6, . . . }. > [Maths Dictionary | Simple Maths | Sums Simple is key stage maths made easy](http://www.sumssimple.com/maths-dictionary.html) I’m forced to believe that your memory is just plain wrong. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 9, 2007, 2:35am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/5 "2007-10-09T02:35:17Z")
More generally, we speak of two numbers a and b being congruent mod m if a - b is divisible by m. This has some really nice properties (and generalizes further in a nice way, but that’s getting pretty far afield). We define the even numbers to be those that are congruent to 0 mod 2 and the odd to be those that are congruent to 1 mod 2. ---
**Author:** ![Polycarp](https://avatars.discourse-cdn.com/v4/letter/p/82dd89/32.png) [@Polycarp](https://boards.straightdope.com/u/Polycarp)\ **Post date:** [October 9, 2007, 3:02am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/6 "2007-10-09T03:02:52Z")
I have no clue where you might have gotten that factoid. But AFAIK there’s no validity in it. What might be the case is a faulty memory of the singularity: One is not prime, by arbitrary rule (and because one being prime would muck up some important premises in number theory), despite the fact that it meets the casual everyday definition of prime (“Evenly divisible only by itself and 1.”) However, the unique character of primes is that they and only they have exactly two and only two discrete natural factors: themselves, individually, and 1. One is completely unique in being the only number with only one discrete natural factor. Not having precisely two discrete natural factors, one is not prime. Rather obviously, two is the only even prime, since “even” means “divisible by 2 within the natural numbers” and hence any other even number would exhibit more than two possible natural factors: 1, 2, and at minimum itself (the case with 4), more often itself and itself-divided-by-two, e.g. 46 (factors of 1, 2, 23, 46). ---
**Author:** ![Siam\_Sam](https://avatars.discourse-cdn.com/v4/letter/s/d78d45/32.png) [@Siam\_Sam](https://boards.straightdope.com/u/Siam_Sam)\ **Post date:** [October 9, 2007, 3:07am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/7 "2007-10-09T03:07:58Z")
I was taught that 1 is odd and 2 even. ---
**Author:** ![Rick](https://avatars.discourse-cdn.com/v4/letter/r/9f8e36/32.png) [@Rick](https://boards.straightdope.com/u/Rick)\ **Post date:** [October 9, 2007, 4:48am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/8 "2007-10-09T04:48:27Z")
[QUOTE=Exapno Mapcase] The one exception I can think of is the elementary definition of an odd number - a number that leaves a remainder of 1 when divided by 2 - which obviously would leave 1 out. [/QUOTE] 😕 1 divided by 2 = 0 with a remainder of 1 ---
**Author:** ![MaceMan](https://avatars.discourse-cdn.com/v4/letter/m/4bbf92/32.png) [@MaceMan](https://boards.straightdope.com/u/MaceMan)\ **Post date:** [October 9, 2007, 5:19am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/9 "2007-10-09T05:19:58Z")
I’m positive 😉 what you are thinking of is the fact that 0 and 1 are “neither prime nor composite,” and that 2 is the only even prime. ---
**Author:** ![maggenpye](https://avatars.discourse-cdn.com/v4/letter/m/ecc23a/32.png) [@maggenpye](https://boards.straightdope.com/u/maggenpye)\ **Post date:** [October 9, 2007, 5:47am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/10 "2007-10-09T05:47:15Z")
[QUOTE=Rick] 😕 1 divided by 2 = 0 with a remainder of 1 [/QUOTE] Alright, I think you’re the person to ask. Since I was 12, I wondered if the fraction; 1 over infinity = 0 my maths teacher said it didn’t but couldn’t explain \*why \*it isn’t. Why isn’t it? and I hope it makes your brain hurt like mine did after reading your sum 😛 ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [October 9, 2007, 5:52am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/11 "2007-10-09T05:52:36Z")
We’ve had that 1/infinity discussion before and the related 1/0=infinity discussion. The problem is that infinity isn’t a number. If 1/infinity=0, what does 2/infinity equal? Zero again, right? So if we treat infinity as just another number then 1=2. So then we have to say that infinity can’t be used in regular old algebra, and that means that expressions like 1/infinity aren’t well defined. ---
**Author:** ![maggenpye](https://avatars.discourse-cdn.com/v4/letter/m/ecc23a/32.png) [@maggenpye](https://boards.straightdope.com/u/maggenpye)\ **Post date:** [October 9, 2007, 5:58am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/12 "2007-10-09T05:58:50Z")
So, if 1/infinity is 0 and 2/infinity is zero, then 1=2. Therefore infinity is not a number (or at least, not a \*defined \*number.) Okay - I get that, though I feel like you’ve just proved black=equals white and I should watch out at the next zebra crossing! ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [October 9, 2007, 8:08am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/13 "2007-10-09T08:08:36Z")
I kind of get the impression that the OP might be confusing this with the (reasonably common) question on whether 1 is considered prime or not. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [October 9, 2007, 9:10am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/14 "2007-10-09T09:10:49Z")
[QUOTE=maggenpye] Alright, I think you’re the person to ask. Since I was 12, I wondered if the fraction; 1 over infinity = 0 my maths teacher said it didn’t but couldn’t explain \*why \*it isn’t. Why isn’t it? [/QUOTE] Because he was waiting for you to reach basic Calculus, probably, when limits and such are introduced. As the denominator approaches infinity, the overall fraction approaches zero, but since the first condition is never actually fulfilled, neither is the second. For _practical_ purposes, though, it’s zero. ---
**Author:** ![Dervorin](https://avatars.discourse-cdn.com/v4/letter/d/eb8c5e/32.png) [@Dervorin](https://boards.straightdope.com/u/Dervorin)\ **Post date:** [October 9, 2007, 10:23am UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/15 "2007-10-09T10:23:23Z")
[QUOTE=Exapno Mapcase] The one exception I can think of is the elementary definition of an odd number - a number that leaves a remainder of 1 when divided by 2 - which obviously would leave 1 out. [/QUOTE] Why would that leave 1 out? 2 goes into 1 zero times with a remainder of 1 - it’s perfectly consistent. ---
**Author:** ![Keeve](https://avatars.discourse-cdn.com/v4/letter/k/f07891/32.png) [@Keeve](https://boards.straightdope.com/u/Keeve)\ **Post date:** [October 9, 2007, 12:12pm UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/16 "2007-10-09T12:12:10Z")
[QUOTE=Polycarp] I have no clue where you might have gotten that factoid. … What might be the case is a faulty memory of the singularity: One is not prime,… [/QUOTE] Pretty much exactly what I was going to suggest. Thanks! ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [October 9, 2007, 3:53pm UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/17 "2007-10-09T15:53:23Z")
[QUOTE=MaceMan] I’m positive 😉 what you are thinking of is the fact that 0 and 1 are “neither prime nor composite,” and that 2 is the only even prime. [/QUOTE] That’s my guess too, particularly since the OP mentioned **positive** integers. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [October 9, 2007, 3:59pm UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/18 "2007-10-09T15:59:40Z")
[QUOTE=Dervorin] Why would that leave 1 out? 2 goes into 1 zero times with a remainder of 1 - it’s perfectly consistent. [/QUOTE] When I said “elementary” definition I was referring to the definition as taught in elementary school - at least back in my time - before classes got to the complexity of getting zero times for an answer. I also said it was wrong. It was a WAG as to why the OP might be remembering 1 as not odd, not a formal expression of math. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [October 9, 2007, 4:21pm UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/19 "2007-10-09T16:21:06Z")
It may not be the OP’s faulty memory. There really are elhi teachers out there that believe this sort of nonsense and pass it on to their students. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [October 9, 2007, 4:28pm UTC](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023/20 "2007-10-09T16:28:34Z")
[QUOTE=maggenpye] So, if 1/infinity is 0 and 2/infinity is zero, then 1=2. Therefore infinity is not a number (or at least, not a \*defined \*number.) Okay - I get that, though I feel like you’ve just proved black=equals white and I should watch out at the next zebra crossing! [/QUOTE] Well think of it this way. 6/2=3, that means the inverse of that is 3\*2=6. So if 1/infinity=0, then 0_infinity=1. But if 2/infinity=0, then 0_infinity=2. Therefore, 1=2. [Next page](https://boards.straightdope.com/t/is-1-an-odd-number-is-2-even/422023.md?page=2)