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You are not logged in. #1 20060327 06:06:53
Proving rational inversesI need to prove that every element of Q (rational numbers) has an inverse with respect to addition. From what understand, I need to use the fact that [0,1] is the additive identity of Q. However, I have no idea what to do beyond that. Last edited by Kazy (20060327 06:07:45) #2 20060327 07:35:09
Re: Proving rational inverses
0 is the additive identity of Q. And you can have 1 and only 1 additive identity.
[1,1] is better written as just 1. The only rational number that doesn't have a multiplicative inverse is 0. Consider a/b where a and b are integers and a and b are nonzero. Then a/b * b/a = 1, and thus, all nonzero rationals have a multiplicative inverse. Last edited by Ricky (20060327 07:36:04) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 