is 0 even or odd?

[rickynumber24]

I'm in math class right now, and when I saw the title of this thread, I immediately asked my math teacher:

"Hey, miss, I have a question."
"I have an answer."
"Is zero even or odd?"
"Oh... ummm... It's negative!"

I have to say, this saddens me more than some of the confusion of mathematical ideas demonstrated in this thread.

 

[Treefingers]

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.

 

[Coldie]

Math doesn't define whatever it wants, any more than something like physics does. The symbols that explain what's going on may be invented as representations of things, but that's it. We didn't "invent" the number pi, we discovered it as a constant factor in mathematics.

Oh yes it does. Numbers are just tools. They are completely optional in math, you can use any symbols you want. Next, "basic" things such as "addition" and "multiplication" are just words, the operations themselves can be defined however you want them to be defined. I can make 2 * 7 = 0 if I construct the appropriate ring. Where does that come up in "reality", hmm? Rules (such as commutativity) are completely optional - a * b does not have to equal b * a if I do not want it to. I declare that "even" in my system means that number has a binary representation with more 0s than 1s and the sky does. not. tremble.

Physics often frowns on casual redefinition of operations and rulesets, but sufficiently advanced math is indistinguishable from magic.

 

[Sparrow]

I love how such an simple question has spawned such debate and yet the guy who posted it still gets a low content post warning.

Regardless... well, I thought it was even before but reading some of these answers has put me off. If 0 isn't a number, is a negative number also not a number but the absence of value? I always figured it was simple in the fact that it goes even(0), odd(1), even(2), odd(3) ect..

 

[crudus]

What is more shocking the lack of use of a search bar. Although on a forum not using a search bar is to be expected but if you just google the question you get the answer.

OP just wanted to post a "controversial" thread to get a lot of posts.

I'm just a college student majoring in computer engineering and this is making me want to strangle something XP

I wonder about how far the people in this thread have gone in math...

It seems people who have had math beyond high school are actually saying intelligent things. I have gotten to Calculus 3, but I have spoken to many people about things like set theory and higher math. I have forgotten most of it -_-

Fair enough. Our maths department is one of the "If you try to index zero in the natural numbers you WILL be beaten to death with a proof by induction" ones. I don't know how it's taught elsewhere, but I did not want to cross the man with the huge wad of proofs.

Yeah, best to not mess with that. I think I was taught that 0 is not a natural number. It all depends on where you want to start anyway. I personally prefer Ribenboim stance personally (if it is convenient to make 0 natural, do so).

Its a human construct designed to show the lack of a presence rather than an actual presence. It can't do anything. You don't ever have zero anything. You just dont have said thing.

ok then what are other numbers if not human constructs?

I love how such an simple question has spawned such debate and yet the guy who posted it still gets a low content post warning.

1. He didn't provide what he thought.
2. He did it to start this debate and for no other reason.

 

[drummond13]

Math doesn't define whatever it wants, any more than something like physics does. The symbols that explain what's going on may be invented as representations of things, but that's it. We didn't "invent" the number pi, we discovered it as a constant factor in mathematics.

Oh yes it does. Numbers are just tools. They are completely optional in math, you can use any symbols you want. Next, "basic" things such as "addition" and "multiplication" are just words, the operations themselves can be defined however you want them to be defined. I can make 2 * 7 = 0 if I construct the appropriate ring. Where does that come up in "reality", hmm? Rules (such as commutativity) are completely optional - a * b does not have to equal b * a if I do not want it to. I declare that "even" in my system means that number has a binary representation with more 0s than 1s and the sky does. not. tremble.

Physics often frowns on casual redefinition of operations and rulesets, but sufficiently advanced math is indistinguishable from magic.

Um, no. 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.

Of course you can call "even" whatever you want. But as it's defined in math right now, 0 is even. Sure, you can say that men "made up" that concept of even, but all we did was name it. The mathematical concept always existed. Just because we could have given it a different name doesn't change anything.

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

 

[Atheist.]

I get a good kick out of reading this thread. People calling one another out with hilarious proofs and "understanding" of math. Failing to realize the difference between a number and an integer, providing fail-proofs, such as defining a number by a function, or using first grader logic as a proof (-1 is odd, 1 is odd, so zero should be as well.) I seriously question the demographic of this site sometimes. I don't see how some of these people graduated high school. Good times. X.x

I am actually a bit confused by your definition as I might be reading it wrong but are you saying that 0 is odd because it is between two odd numbers?

Actually I never defined it. I was simply mocking some posts with fail reasoning I saw. I guess I should have said -1 is odd and 1 is odd so 0 should be even. But that itself is a poor way to define zero as even. Zero is even because it is divisible by two. Not much more to say on this topic.

 

[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

It's really easy to divide an even amount by an odd amount in many cases. 2/5, for instance is exactly .4

Also, both 1 and 3 are odd, so I don't see how your argument about an even amount being divided by an odd amount applies to the 1/3.

Finally, 1/3 is exactly .3 recurring. It's easy enough to demonstrate, just do it in long division and you'll quickly see that it iterates infinitely. A decimal point followed by any finite number of 3s is only an approximation, true, but an infinite number of 3s is an exact decimal representation of one third. It's why recurring notation was invented, so we could represent repeating non-terminating decimals.

 

[Tzekelkan]

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.

 

[Glademaster_v1legacy]

I get a good kick out of reading this thread. People calling one another out with hilarious proofs and "understanding" of math. Failing to realize the difference between a number and an integer, providing fail-proofs, such as defining a number by a function, or using first grader logic as a proof (-1 is odd, 1 is odd, so zero should be as well.) I seriously question the demographic of this site sometimes. I don't see how some of these people graduated high school. Good times. X.x

I am actually a bit confused by your definition as I might be reading it wrong but are you saying that 0 is odd because it is between two odd numbers?

Actually I never defined it. I was simply mocking some posts with fail reasoning I saw. I guess I should have said -1 is odd and 1 is odd so 0 should be even. But that itself is a poor way to define zero as even. Zero is even because it is divisible by two. Not much more to say on this topic.

Ok I just wasn't sure if I was reading it wrong or whatever.

What is more shocking the lack of use of a search bar. Although on a forum not using a search bar is to be expected but if you just google the question you get the answer.

OP just wanted to post a "controversial" thread to get a lot of posts.

I got that but the sheer staggering amount of people posting with bad answers and that dodgy algebra proof everytime this comes up makes my head want to explode.

 

[[.redacted]]

I think this isn't a question, but a survey of the average escapist's intelligence.

"You can't divide it by anything" --- Really? 0/1 = 0
"It's just a concept" --- So is the number 1
"It's the lack of a number" --- But it still functions in the same way as other numbers

It's even.

 

[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.