is 0 even or odd?

[Thundero13]

0 is even because it is inbetween 2 odd numbers ie 1 & -1

 

[Glademaster_v1legacy]

0.9*recurring is not equal to 1 because no matter how infinitesimally small the difference is, the difference exists.

And 0 is a number and a digit and an integer (ask any programmer) and it IS even.

1/3 = .33(recurring). Multiply both sides by 3.

3/3=.99(recurring)

So unless you care to argue that three thirds is less than 1, .9 recurring is equal to 1.

.99 repeating is approximately 1, it is never and has never actually been equal to 1, and 1/3 is approximately .33 repeating, it is not actually possible to divide and even amount of something by an odd amount of something which is why we approximate it

If you want I can prove it with an infinite Geometric Series which does leave the dodgy hole in the algebra proof.

 

[bojac6]

Jesus, people. 0.999... = 1 is true. There is no difference between them.

You could say that there is, but there really isn't, not a real one. The only "difference" that you could spot would be after spending an infinite amount of time looking for it. But that's physically impossible. No, not just unlikely, but physically impossible.

The age of the Universe is about 13 billion years. That is a finite amount. It would take an infinite more amount of time to spot the difference between 0.999... and 1. And if anything takes an infinite amount of time, that doesn't just mean that for all intents and purposes it cannot be done, but it just physically cannot be done.

Take, say, an atom that has an infinite lifetime. That means it takes an infinite amount of time for it to disintegrate. Would you say it is an unstable atom? No, you would not. It is stable, because there is no difference between unstable with an infinite lifetime and stable. No physical, philosophical, mathematical difference.

Same with 0.999... = 1. It's just two different ways of writing the same concept, the number 1.

You're absolutely right. I like that analogy, I hadn't heard it before.

A more technical way of saying it is that if there is a difference between .99... and 1, then you are quantifying infinity, because whatever the difference between .9999... and 1 is, that is a quantity which represents the end of infinity. Since that is impossible by definition, there can be no difference between .999... and 1.

 

[Rofl-Mayo]

If one is odd then the number that comes before it must be even. 0 is even.

 

[crudus]

No it is not a mathematical fact, it is a fallacy pure and simple

this AGAIN? seriously, pack that shit in! it's not true. 0.9 recurring = 0.9 recurring, 1 = 1.

besides, I think there's a flaw in your third step. how is 9 * 0.9*recurring equal to 9? it would be equal to 8.9*recurring if my brain works (probably doesn't right now) but I'm pretty sure 9*0.9*recurring is NOT equal to 9. because if it was, you're already assuming 0.9*recurring = 1, before having proven it.

so there is a difference and no amount of flawed mathematics are going to convince me any different.

While I agree with you that I don't want to see the again you are supposed to do it with variables. It looks incredibly messy that way.

Spoiler: This is how you are supposed to do it

Spoiler: Although this was is much simpler

Spoiler: Although my favorite...

And sufficiently advanced math is magic? I suppose it must look like it to you.

I have actually had it explained to me that way by professors and grad students before. Although it is said mostly flippantly.

Jesus, people. 0.999... = 1 is true. There is no difference between them.

There was also another thread about this where nothing different was said.

 

[fuzzygenius]

An element of the integers is even if it is divisible by 2. In other words, is 0/2 an integer. Even more precisely, is there an integer n such that 0 = 2*n. There is such an n - let n = 0.

Hence, 0 is even.

Alternatively, we can define the even integers to be all integers in the set {2k | k is an integer}, but that feels like cheating a little. (Equivalently, define the evens to be all elements of Z/2Z, to bring in some group theory).

And again, we could also define n to be even if n is congruent to 0, modulo 2. Hence, 0 is even.

Oh, and assuming you're willing to agree that all integers are numbers, then 0 is a number - if the integers must include 0, or Z would fail to be an additive group.

And all this assumes you're talking about 0 the mathematical object, not as a philosophical concept of nothingness (although if you're talking about parity, then it seems reasonable to assume you're talking about 0 the mathematical object).

I believe you want 2Z, not Z/2Z. Z/2Z has a total of 2 elements. (By the way, it makes more sense to deal with rings here.)

Ah, yes. Serves me right, posting too late at night.

 

[bojac6]

0.9*recurring is not equal to 1 because no matter how infinitesimally small the difference is, the difference exists.

And 0 is a number and a digit and an integer (ask any programmer) and it IS even.

1/3 = .33(recurring). Multiply both sides by 3.

3/3=.99(recurring)

So unless you care to argue that three thirds is less than 1, .9 recurring is equal to 1.

.99 repeating is approximately 1, it is never and has never actually been equal to 1, and 1/3 is approximately .33 repeating, it is not actually possible to divide and even amount of something by an odd amount of something which is why we approximate it

If you want I can prove it with an infinite Geometric Series which does leave the dodgy hole in the algebra proof.

Are you referring to the proof with the limit of x approaching infinity in 1/10^x ?

Also, what's the dodgy hole in the algebra proof? It's pretty straightforward and accurate.

 

[Coldie]

Of course you can change the words and symbols if you want, but the concepts behind them remain constant. Sure, you can call "addition" something else and "subtraction" something else (and other languages do), but that doesn't change the fact that there are such things as what we call addition and subtraction.

"Addition" and "multiplication" are extremely common operations (while "subtraction" and "division" are not so much), they even have their own, specific, definitions. The symbols that denote those two operations are commonly used, as well, but beyond that everything is defined by the source material. The operands are not necessarily numbers, for instance. They also could be vectors, n-dimensional matrices, other sets, polynomials, functions... maybe even whole other Theories, if you want to go meta.

As for the core operation itself, addition for the layman is quite different from addition in, say, ring Z/Z[sub]14[/sub], to say nothing of multiplication (yay for Zero Divisors). The things we call "addition" and "subtraction" in everyday life we use with an implied qualifier "in the ring of Real numbers" or "integers" or somesuch, depending on context.

Look up "Algebra" for the general information on groups or "Ring theory" to go straight to Rings. This is common university-level material.

And sufficiently advanced math is magic? I suppose it must look like it to you.

I'm the wizard, I do the magic and it's glorious. Even the simplest math tricks - such as "0 is even" or "0.(9) = 1" or "e[sup]i*Pi[/sup] + 1 = 0" or "Monty Hall, switch" - never fail to baffle hundreds of math-challenged individuals. Shazam.

 

[Glademaster_v1legacy]

0.9*recurring is not equal to 1 because no matter how infinitesimally small the difference is, the difference exists.

And 0 is a number and a digit and an integer (ask any programmer) and it IS even.

1/3 = .33(recurring). Multiply both sides by 3.

3/3=.99(recurring)

So unless you care to argue that three thirds is less than 1, .9 recurring is equal to 1.

.99 repeating is approximately 1, it is never and has never actually been equal to 1, and 1/3 is approximately .33 repeating, it is not actually possible to divide and even amount of something by an odd amount of something which is why we approximate it

If you want I can prove it with an infinite Geometric Series which does leave the dodgy hole in the algebra proof.

Are you referring to the proof with the limit of x approaching infinity in 1/10^x ?

Also, what's the dodgy hole in the algebra proof? It's pretty straightforward and accurate.

0.999999.... = 9(10) + 9(10)[sup]2[/sup] + 9(10)[sup]3[/sup]......= 9(1/10) / (1 - 1/10) = 1

If that is the start of the one you think I am talking about then yes and the main flaw with the algebra on is the 9x=9. Yes it works but it assumes the person understands that 0.999... is one as if you were to multiply part of 0.99999 by 9 you will 8.999991 or something like that.

With the infinite Geometric series proof there is no come back not that there really is in the algebra one this just leaves no questions.

 

[Amondren]

Neither.... zero is not a number, but a lack there of.

This is the answer if you ask any math teacher/professor and I agree with it.

I asked a math professor and he told me that you made that up just then.

Ok man chill out.

 

[bojac6]

0.9*recurring is not equal to 1 because no matter how infinitesimally small the difference is, the difference exists.

And 0 is a number and a digit and an integer (ask any programmer) and it IS even.

1/3 = .33(recurring). Multiply both sides by 3.

3/3=.99(recurring)

So unless you care to argue that three thirds is less than 1, .9 recurring is equal to 1.

.99 repeating is approximately 1, it is never and has never actually been equal to 1, and 1/3 is approximately .33 repeating, it is not actually possible to divide and even amount of something by an odd amount of something which is why we approximate it

If you want I can prove it with an infinite Geometric Series which does leave the dodgy hole in the algebra proof.

Are you referring to the proof with the limit of x approaching infinity in 1/10^x ?

Also, what's the dodgy hole in the algebra proof? It's pretty straightforward and accurate.

0.999999.... = 9(10) + 9(10)[sup]2[/sup] + 9(10)[sup]3[/sup]......= 9(1/10) / (1 - 1/10) = 1

If that is the start of the one you think I am talking about then yes and the main flaw with the algebra on is the 9x=9. Yes it works but it assumes the person understands that 0.999... is one as if you were to multiply part of 0.99999 by 9 you will 8.999991 or something like that.

With the infinite Geometric series proof there is no come back not that there really is in the algebra one this just leaves no questions.

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.

 

[Hagi]

0.999999.... = 9(10) + 9(10)[sup]2[/sup] + 9(10)[sup]3[/sup]......= 9(1/10) / (1 - 1/10) = 1

If that is the start of the one you think I am talking about then yes and the main flaw with the algebra on is the 9x=9. Yes it works but it assumes the person understands that 0.999... is one as if you were to multiply part of 0.99999 by 9 you will 8.999991 or something like that.

With the infinite Geometric series proof there is no come back not that there really is in the algebra one this just leaves no questions.

I like this one, much more elegantly shaped. Hadn't seen it before.

 

[drummond13]

Of course you can change the words and symbols if you want, but the concepts behind them remain constant. Sure, you can call "addition" something else and "subtraction" something else (and other languages do), but that doesn't change the fact that there are such things as what we call addition and subtraction.

"Addition" and "multiplication" are extremely common operations (while "subtraction" and "division" are not so much), they even have their own, specific, definitions. The symbols that denote those two operations are commonly used, as well, but beyond that everything is defined by the source material. The operands are not necessarily numbers, for instance. They also could be vectors, n-dimensional matrices, other sets, polynomials, functions... maybe even whole other Theories, if you want to go meta.

As for the core operation itself, addition for the layman is quite different from addition in, say, ring Z/Z[sub]14[/sub], to say nothing of multiplication (yay for Zero Divisors). The things we call "addition" and "subtraction" in everyday life we use with an implied qualifier "in the ring of Real numbers" or "integers" or somesuch, depending on context.

Look up "Algebra" for the general information on groups or "Ring theory" to go straight to Rings. This is common university-level material.

And sufficiently advanced math is magic? I suppose it must look like it to you.

I'm the wizard, I do the magic and it's glorious. Even the simplest math tricks - such as "0 is even" or "0.(9) = 1" or "e[sup]i*Pi[/sup] + 1 = 0" or "Monty Hall, switch" - never fail to baffle hundreds of math-challenged individuals. Shazam.

Touche. Anything is magic with this kind of audience.

 

[drummond13]

Neither.... zero is not a number, but a lack there of.

This is the answer if you ask any math teacher/professor and I agree with it.

I asked a math professor and he told me that you made that up just then.

Ok man chill out.

Um...he seemed pretty chill there, actually.

 

[Ishadus]

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.

 

[Glademaster_v1legacy]

0.9*recurring is not equal to 1 because no matter how infinitesimally small the difference is, the difference exists.

And 0 is a number and a digit and an integer (ask any programmer) and it IS even.

1/3 = .33(recurring). Multiply both sides by 3.

3/3=.99(recurring)

So unless you care to argue that three thirds is less than 1, .9 recurring is equal to 1.

.99 repeating is approximately 1, it is never and has never actually been equal to 1, and 1/3 is approximately .33 repeating, it is not actually possible to divide and even amount of something by an odd amount of something which is why we approximate it

If you want I can prove it with an infinite Geometric Series which does leave the dodgy hole in the algebra proof.

Are you referring to the proof with the limit of x approaching infinity in 1/10^x ?

Also, what's the dodgy hole in the algebra proof? It's pretty straightforward and accurate.

0.999999.... = 9(10) + 9(10)[sup]2[/sup] + 9(10)[sup]3[/sup]......= 9(1/10) / (1 - 1/10) = 1

If that is the start of the one you think I am talking about then yes and the main flaw with the algebra on is the 9x=9. Yes it works but it assumes the person understands that 0.999... is one as if you were to multiply part of 0.99999 by 9 you will 8.999991 or something like that.

With the infinite Geometric series proof there is no come back not that there really is in the algebra one this just leaves no questions.

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.

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.

0.999999.... = 9(10) + 9(10)[sup]2[/sup] + 9(10)[sup]3[/sup]......= 9(1/10) / (1 - 1/10) = 1

If that is the start of the one you think I am talking about then yes and the main flaw with the algebra on is the 9x=9. Yes it works but it assumes the person understands that 0.999... is one as if you were to multiply part of 0.99999 by 9 you will 8.999991 or something like that.

With the infinite Geometric series proof there is no come back not that there really is in the algebra one this just leaves no questions.

I like this one, much more elegantly shaped. Hadn't seen it before.

It is a nice proof I just prefer it over the algebra one as it leaves out any confusion over 9x = 9.

 

[funguy2121]

I remember when we nerds were supposed to be considered intelligent. What happened to that? When did we start using wikipedia as the gold standard? I changed wikipedia 2 months ago, knowing it was bullshit - wikipedia is not a gold standard.

Then use the gold standard to disprove it. That's actually how sourcing something works...

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.

 

[funguy2121]

It's even.

A number is even if it is divisible by 2 with no remainder.

I really hope you dont honestly believe that.

...Wikipedia [http://en.wikipedia.org/wiki/Parity_of_zero] agrees with me, sir.

I remember when we nerds were supposed to be considered intelligent. What happened to that? When did we start using wikipedia as the gold standard? I changed wikipedia 2 months ago, knowing it was bullshit - wikipedia is not a gold standard.

Every website bar 1 on the first page of googling is 0 even or odd comes up with even and in this case the Wiki article is right and so is my maths book. Also so is observation.

Thanks for letting me know. Wikipedia is still not, on its own, a reliable source of information.

 

[drummond13]

I remember when we nerds were supposed to be considered intelligent. What happened to that? When did we start using wikipedia as the gold standard? I changed wikipedia 2 months ago, knowing it was bullshit - wikipedia is not a gold standard.

Then use the gold standard to disprove it. That's actually how sourcing something works...

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.

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]

I remember when we nerds were supposed to be considered intelligent. What happened to that? When did we start using wikipedia as the gold standard? I changed wikipedia 2 months ago, knowing it was bullshit - wikipedia is not a gold standard.

Then use the gold standard to disprove it. That's actually how sourcing something works...

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.

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.

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.

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.