is 0 even or odd?

[LordDarkPhantom]

After trawling through the Internet and consulting ten different mathematicians, I can now conclude that the number 0 is actually oden, which is a hybrid of even and odd.

/thread

 

[Rafael Dera]

Zero is an even number. An integer n is called *even* if there exists
an integer m such that n = 2m, and *odd* if n+1 is even. From this,
it is clear that 0 = (2)(0) is even. The reason for this definition
is so that we have the property that every integer is either even or
odd.

from http://mathforum.org/library/drmath/view/57104.html

 

[artanis_neravar]

No, the guy you quoted is right, 10*.9999=9.999, 9.999-.9999=8.999 and 9*.999=8.999, which does not equal 9, you can not use your argument in a proof to say that 8.999 is close enough to 9

Wait so if (9.999... - 0.999... = 8.999....) then what is (9.999... - 1)?

It can't be 8.999... because that would mean 0.999... was equal to 1 anyway, so it must be something else? What is it then?

Sorry 8.9991, and there is one less 9 after the decimal in the 9.999 than in the 0.9999

 

[drummond13]

Not starting with real life concepts to get new theorems just saves on time, because reality, like math, has immutable laws (and if it doesn't then reality is a lie).

Which is why philosophy can actually have purely abstract notions in it. Math's rules are limited by reality...

Math does not have immutable laws. Math literally defines whatever laws it damn wants. Real world, not so much. When I create a mathematical system, I decide whether or not multiplication is possible, if it is, how does it work, how (if at all) it can be reversed, or how many divisors will zero have [that is, a*b = 0, where a != 0 and b != 0]. I define the aleph and the omega, not the "real world". Math can do it. Philosophy and Physics cannot do it.

Real world has no benefit from knowing that there are exactly as many numbers p/q (where p,q are both positive integers numbers) as there are positive integers or that there are exactly as many numbers between (0, 1) as there are Real numbers, but in math world it amounts to at least 3 nerdgasms each month. Euler's Identity (as seen in my avatar) pulls that many per hour.

Philosophy is a collection of abstract concepts that are grounded in and applied to reality. Math has no such constraints, you define them yourself. When other disciplines use maths, they do it on their own terms, use their own axioms and rules to construct the mathematical model.

Be as it may, the end doth remain: do not look for a connection that does not exist, because you might believe that you've found it.

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.

 

[ZeroDotZero]

Even. I can share 10 slices of cake equally between two people. I can share no slices of cake equally between two people. This makes them both even.

 

[GeorgW]

It's odd. What are all of you talking about, it's so obvious!

 

[drummond13]

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

10 * 0.9*recurring = 9.9*recurring. (simply switch the decimal point one place as always when multiplying by ten)
9.9*recurring - 0.9*recurring = 9. (beyond the decimal point these numbers are identical.)
10 * 0.9*recurring - 0.9*recurring = 9 * 0.9*recurring = 9. (10 * a - a = 9 * a. By the definition of multiplication.)
9 * 0.9*recurring = 9 * 1.
0.9*recurring = 1.

No difference at all. Not even an infinitely small one.

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.

This isn't flawed mathematics. And there are several other proofs of this out there. Look them up.

This is math. Just because you don't believe it's true doesn't make it any less true. You look more than a little silly when you so fervently deny something like this.

No, the guy you quoted is right, 10*.9999=9.999, 9.999-.9999=8.999 and 9*.999=8.999, which does not equal 9, you can not use your argument in a proof to say that 8.999 is close enough to 9

(sigh) It's not "close enough" to 9. It is exactly equal to 9.

Look, I know this is kind of a mind@#$% of a concept. I get that. But this is a mathematical fact. This isn't theoretical. There can be no debate about this, any more than someone can debate what the value of pi is.

This has already been proven several times over in this thread, and there are other proofs out there. Look them up. Learn something.

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

....Okay, then please prove it. Since you so clearly understand math. We've already had several proofs that it ISN'T a fallacy, I'd absolutely love to see proof that it is. Other than you simply STATING that it is.

 

[F'Angus]

Argh *brain explodes*

but

Um...if I remember right, it's even. Everybody get's nothing.

- this seems like the best answer

 

[Hagi]

Sorry 8.991, and there is one less 9 after the decimal in the 9.999 than in the 0.9999

We're talking about infinite 9's. Not a limited number. Infinite. If you multiply a number with infinite decimals by 10 then it will still have infinite decimals.

And where the hell did you get that '1' in 8.991 from? And how exactly did that number suddenly stop having infinite decimals? What kind of rules are you using? "a - b = whatever I want"?

 

[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.