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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

I was trying to prove the propositions that follow the addition axioms as a revision, I got a different proof for the following proposition:

If $x+y=x+z$ then $y=z$

My proof was the following:

$x+y=x+z$, $(-x)+x+y=(-x)+x+z$, $0+y=0+z$, $y=z$

Rudin however, in his book, provides a different proof:

$y=0+y=(-x+x)+y=-x+(x+y)=-x+(x+z)=(-x+x)+z=0+z=z$

This is how I was thinking, I start from the condition, to reach the result. Is my proof incorrect?

Thanks!