is 0 even or odd?
- Thread starter Drakmeire
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I like the 1/9 = .1 repeating, then multiply by 9, which also avoids that hole. But you make a good point, the biggest flaw in any of these proofs (including the geometric one) is that the person you're explaining it to might not understand it. If they had a firm grasp of mathematics, they'd already understand why it's right and wouldn't need you to argue with them.Glademaster said:
I've never wanted to laugh out loud and facepalm my face into the ceiling simultaneously so hard before. But, at 11 pages long, all the arguments to be made proving that 0 is an even integer have already been made.
I wonder how much of these misunderstandings are caused because people use the term "number" and "integer" interchangeably without understanding the difference (or perhaps not knowing what integer means at all). God forbid a question ever got asked that used the terms "number," "integer," "natural number," "rational number," "irrational number," etc.
I wonder how many people in the world win a lottery or a contest or something, but can't claim their prize because they fail the skill testing question.
I wonder how much of these misunderstandings are caused because people use the term "number" and "integer" interchangeably without understanding the difference (or perhaps not knowing what integer means at all). God forbid a question ever got asked that used the terms "number," "integer," "natural number," "rational number," "irrational number," etc.
I wonder how many people in the world win a lottery or a contest or something, but can't claim their prize because they fail the skill testing question.
I suppose you would have to know of the formula (a)/(1-r) but I still think it cuts the BS out of 9x =/= 9.bojac6 said:
It is a nice proof I just prefer it over the algebra one as it leaves out any confusion over 9x = 9.Hagi said:
Wikipedia is not a reliable source of information, no matter how snooty you are when you source it. That's how reliable information works. Zero is not an integer.4li3n said:
Thanks for letting me know. Wikipedia is still not, on its own, a reliable source of information.Glademaster said:
True, Wikipedia is not 100%. But again, it IS right in this case. 0 is an integer and it IS even. Please explain to us why you disagree if you want to be taken seriously here. You're contradicting a basic rule of math.funguy2121 said:
I explained earlier, as did others on this very page. If 0 being an even number is considered a basic rule of math then it must be a recently new development, and I have yet to see any of you nitty-nit-nit-pickers source anything other than Wikipedia (with "and I say it's correct!" as supporting evidence) and other forums. I could similarly claim that "My Little Pony sucks!" and as support, link to another Escapist thread or a 4Chan forum entitled just that. This would not, however, make my case.drummond13 said:
And being taken seriously by those who would argue over whether 0 is an even number for 11 pages is not chief among my concerns.
0 is not 2, nor is it a multiple of 2. Present to me an argument that doesn't begin with "if you assume that..." and we'll talk. Until then, 0 not =ing 2 or a multiple thereof is enough for me to not consider it an even number just because someone on the internet (who isn't a mathematician) said so.
Patronize me one more time and you run the serious risk of being Fez'd.
Algebraic proof: You interchange multiplication and infinite summation - 10x sum(9x0.1^n) = sum(10x9x0.1^n) which I'd avoid - to avoid that you'd have to deal with limits.
For the geometric series proof you, again, assume the result than sum(r^n)=(1-r)^-1 which also requires limits - if people don't believe that 0.9* = 1 then they'd probably not believe that 1/10 + 1/100 + 1/1000 + ... = 1/9 either.
So if you're going to prove that 1=0.9* you might just as well do it properly. Let epsilon>0, let a_n = sum(9x0.1^k) for k=1 to n. Then there is an N st for n>N, |a_n - 1| < epsilon. Hence 0.9* = limit a_n = 1
For the geometric series proof you, again, assume the result than sum(r^n)=(1-r)^-1 which also requires limits - if people don't believe that 0.9* = 1 then they'd probably not believe that 1/10 + 1/100 + 1/1000 + ... = 1/9 either.
So if you're going to prove that 1=0.9* you might just as well do it properly. Let epsilon>0, let a_n = sum(9x0.1^k) for k=1 to n. Then there is an N st for n>N, |a_n - 1| < epsilon. Hence 0.9* = limit a_n = 1
From my formulae and tables book Z(this is the integer set)=(....-3, -2, -1, 0, 1, 2, 3....)funguy2121 said:
No Wiki on its own is not a 100% reliable source. It is good for a quick summary or overview of a topic but if you want to go in depth you usually look at the citations or google for other sources.funguy2121 said:
I stand corrected. 0 is indeed an integer. I must have been thinking Sprockets integers. But how does this make zero "even?" It's not a multiple of 2. It's not even really an amount, just the mathematical symbol for nuthin'.Glademaster said:
I'm glad we agree on Wikipedia. This is why it's ineffective as a tool in a debate. If you have to source something, then look at those sources for verification, and also look to see if management has tagged it for cleanup (assuming they've gotten to it), then it has no real weight as evidence. It does work just fine as a sort of springboard when you're first researching something, though.
Apparently being taken seriously by us IS a concern of yours.funguy2121 said:
The only arguments that have begun with "if you assume that..." are those that then go on to quote the definition of being an even number. By any mathematical definition of what makes an even number even, zero is even. I like how you felt the need to point out that zero was not 2. I must have missed the argument that stated that it was. You don't have to be a mathematician to figure this out.
As for your assertion that zero isn't an integer, well gee, would you like to look up the definition of what an integer is? Again, this isn't exactly a debatable thing.
If you don't want to be patronized, don't say easily disprovable things about math. This isn't a subjective topic. There's only one right answer here and it isn't the one you're arguing so adamantly in favor of.
Ok 0 is a multiple of 2 because it is divisible by 2 without leaving a remainder. Like 2*1=2 but 2/2=1 same as 2*0=0 and 0/2=0. The only thing about 0 is when you multiply by it you get 0. So it is a unique number like when you Multiply 1 by anything you get the same number. The thing of 0 being an integer is important as an Integer must be either odd or even. Also any even number is found by 2A and an odd one is found by 2A - 1. 0 is found with 2A. Although another way of proving it is even is kinda by a cop out. It is between -1 and 1. -1 and 1 are odd numbers so therefore 0 is even as it goes odd even odd or even odd even whichever number at which you start.funguy2121 said:
I hope that clears everything up.
0 is a multiple of 2.funguy2121 said:
0 = 2 * 0
If you don't trush wikipedia, you can ask something that is a "mathematician", of sorts: is 0 an even number? [http://www.wolframalpha.com/input/?i=is+0+an+even+number%3F]
You can ask other stuff, like "is 0 an integer". Or anything, really.
Please love me, please!drummond13 said:
This is as appropriate a situation as any to do it by the numbers, so...
(1) I looked at some sources provided back when this was only a few pages long, and all of them were in comments sections and said, "Well, if you're going based on this... (this being an arbitrary assertion, some of which were thoughtful but not necessarily accurate and none having anything to do with established mathematical rules)" I was clear about this. And asserting that zero is even is not "quoting the definition of zero," Mr. Man.
(2)But you just read, and quoted, and referred to it.
(3)I just recognized my mistake and corrected it, so you may have missed it. But I'm not giving you my number.
(4)What does Wolverine have to do with any of this?
(You were warned. You made me do this!)
1: Plenty of other people have defined both zero and even numbers. I don't feel the need to repeat it all here.funguy2121 said:
2: I have no idea what you mean by this.
3: Very big of you. Maybe now you'll be open to the fact that you're wrong about whether it's even or not as well? I appreciate the desperate hint to ask you for your number but I'm happily engaged.
4: lol. No, seriously, that was actually pretty funny.
I said good day, sir! That's that.drummond13 said:1: Plenty of other people have defined both zero and even numbers. I don't feel the need to repeat it all here.funguy2121 said:
2: I have no idea what you mean by this.
3: Very big of you. Maybe now you'll be open to the fact that you're wrong about whether it's even or not as well? I appreciate the desperate hint to ask you for your number but I'm happily engaged.
4: lol. No, seriously, that was actually pretty funny.