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What do you think is my proof correct?

To prove x.0=0
x.0 = x.0 + 0 (0 is additive identity)
= x.0 + (x + (-x)) (x must have an additive inverse)
= (x.0 + x) + (-x) (by associativity)
= (x.0 + x.1) + (-x) (1 is multiplicative identity)
= x.(0+1) + (-x) (by distributivity)
= x.1 + (-x) (0 is additive identity)
= x + (-x) (1 is multiplicative identity)
= 0 (by definition of additive inverse).
Adrián Juárez Carrasquedo
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1 Answers1

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You should start by stating what you are trying to prove so people know what to expect. It looks like you want to prove $\forall x x\cdot 0=0$ We need to understand what axioms you are using, but it looks fine.

Ross Millikan
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  • .I was trying to prove x*0=0, I didn't notice, I specify the axioms in the parentheses, is it not clear enough?, in which way should I do it? and other question what do you recommend Im never sure if what i prove is correct? – Adrián Juárez Carrasquedo Sep 15 '18 at 03:08
  • Each axiom seem appropriate to the step you are taking. I was referring to the whole set available. In the Peano Axioms for arithmetic $a\cdot 0=0$ is an axiom, so it is silly to prove. The Wikipedia article on the field axioms does not give us that one, so it needs to be proven. That is my point on understanding the axioms that the axioms you are using. – Ross Millikan Sep 15 '18 at 03:15