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 November 11th, 2016, 06:35 AM #1 Newbie   Joined: Nov 2016 From: Europe Posts: 3 Thanks: 0 Fields I'm learning about fields and I still dont get how to prove things in fields, for example 1. F∈a. and I need to prove that if a^2 = 1 , then a = 1 or a= -1 2. if a^2 =a , then a =0 or a = 1 This what I did : 1. a^2 =1 --> a^2 -1 = 0 --> a^2 -1 *1=0 (1 is neutral -axiom)--> a^2 -1^2 --> (a+1)(a-1) = 0 --> a=1 or a=-1 . 2. a^2 - a = 0 --> a*(a-1) = 0 --> a=0 or a= 1. is that good or should I use more fields axioms ?
November 22nd, 2016, 05:56 PM   #2
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 Originally Posted by dave22 I'm learning about fields and I still dont get how to prove things in fields, for example 1. F∈a.
You mean a∈ F.

Quote:
 and I need to prove that if a^2 = 1 , then a = 1 or a= -1 2. if a^2 =a , then a =0 or a = 1 This what I did : 1. a^2 =1 --> a^2 -1 = 0 --> a^2 -1 *1=0 (1 is neutral -axiom)--> a^2 -1^2 --> (a+1)(a-1) = 0 --> a=1 or a=-1 .
Before the last statement, say first that a+ 1= 0 and a- 1= 0. And that is true because F, being a field, does not have "zero divisors".

Quote:
 2. a^2 - a = 0 --> a*(a-1) = 0 --> a=0 or a= 1.
Again, first say that either a= 0 or a- 1= 0.

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 is that good or should I use more fields axioms ?

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