zero

[Gale]

How come zero and onw are so important to our number system? they both have oddities about them that are particular only to them... identy properties, division by zero... and whatnot. Is this because we're in a base 10 system? in say binary... are there special numbers like that? or in a base 12 system?

...should this be in number theory?

[Hurkyl]

Well, something has to be the additive and multiplicative identities. [:)]

Ok, that's not entirely true; not all mathematical structures have to have such identities... but identities are very useful things, and pretty much all of the important algebraic structures have them.



Also, binary, decimal, and base-12 (duodecimal, I think) numbers are all the same numbers... these are just different systems of writing them.

[Gale]

soo... one and zero retain their identitive properties even in other number systems... i suppose that made sense... same numbers... i guess there's no way to get different numbers... but hmm... how about like... i dunno... i have to think some more...

[Hurkyl]

Well, binary, hexadecimal, et cetera are all the same numbers, so 0 and 1 are the same thing in all of them. (They're all written the same way too, of course).


But in other things, such as abstract groups, fields, and vector spaces, we still call the additive and multiplicative identities 0 and 1, but it would be misleading to say they're the "same thing".

[Organic]

0 AND 1 are complementary concepts, and also mutiplication and addition.

Please look here:

http://www.physicsforums.com/showthread.php?s=&threadid=11909

Thank you.


Organic