is 0 even or odd?

[zehydra]

Nothingness cannot be classified into any category or class. It simply isn't.

But Zero isn't nothingness.

And wouldn't the fact that nothingness has attributes such as being unclassifiable, make it have it's own special class of being?

Zero, by definition, is nothing.

rather, Zero, by definition is the lack of a quantity, not "nothing". It is an idea, not the lack thereof

 

[4li3n]

rather, Zero, by definition is the lack of a quantity, not "nothing". It is an idea, not the lack thereof

Dude, that's semantics...

The idea is that no matter what it represents it fits the definition of an even number, and thus is one, especially since there's no reason to make an exception for it as far as math is concerned.

 

[zehydra]

rather, Zero, by definition is the lack of a quantity, not "nothing". It is an idea, not the lack thereof

Dude, that's semantics...

The idea is that no matter what it represents it fits the definition of an even number, and thus is one, especially since there's no reason to make an exception for it as far as math is concerned.

he was basically saying that Zero wasn't a number, which is of course wrong.

 

[riverand]

Neither... Zero is not an integer.

The concept of even and odd only applies to integers therefore 2 is even, 3 is odd, 3.5 is neither and 0 is neither also.

Actually zero is an element in the set of integers (the Z set).

Strictly speaking it's even, since when you do set mappings you use 2*n for evens and 2n+(or -)1 for odds where n is an integer. However the principle of odd and even is only really used in natural number mappings, and 0 is not a natural number. So essentially from an analytical maths perspective it doesn't really matter but for the sake of completeness it's even.

Preach on, Zantos! I'm a high school math teacher practically hyperventilating over here with the responses. You set my mind at ease, I will be able to sleep soundly tonight knowing that your response is out there.

I'm glad I could help. However would it spoil it if I said this is the ONLY time I've ever used set theory outside of an exam?

0 is not a natural number.

Actually that just depends on who you ask. Zero is "sometimes" considered natural. "Natural Number" is actually kind of an ambiguous term to begin with

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.

Zantos, you have ruined nothing. I often share with my students that some of what we will learn will serve them no further than just confusing the heck out of someone later in life, helping young children with their homework, or just to impress upon their parents that they learned something scholarly-sounding during their day at school!

As for this zero as a Natural number debate, Crudus, this is new to me. (Although I am aware that zero does like to be difficult whenever seemingly possible!) I have always believed zero NOT to be a Natural number as the Natural numbers are often also called the counting numbers and you can't count zero. Also, if zero IS a Natural number, what is to distinguish th set of Natural numbers from the set of whole numbers?

 

[4li3n]

he was basically saying that Zero wasn't a number, which is of course wrong.

Sure, but you where saying it wrong...


Of course so was he, because it being a number that represents nothing could easily allow for an exception so that it would be outside of the odd/even dynamic as long as it doesn't affect anything else (of course then the exception would be pointless anyway)... which is what he wanted to argue, that as a number that represents nothing (or a state of rest etc) it's an exception.