How come zero and one are so important to our number system?

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Zero and one are fundamental to our number system due to their unique properties, such as being the additive and multiplicative identities. Their significance extends across various numeral systems, including binary, decimal, and base-12, where they maintain these identities. While these systems represent the same numbers, the roles of zero and one can differ in abstract mathematical structures like groups and fields. The discussion highlights the importance of these identities in algebraic contexts, emphasizing their complementary nature. Overall, zero and one are essential for understanding the foundations of mathematics across different number systems.
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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?
 
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Well, something has to be the additive and multiplicative identities. :smile:

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.
 
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...
 
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".
 

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