Why Use a - b Instead of a + b in Equivalence Classes of Rings?

InquilineKea
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So I'm kind of confused about the definition:

a-b\in I

Why a - b instead of a + b?
 
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Are you trying to prove that a-b is an equivalence relation? Can you be more specific?
 
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It's actually natural to write a-b because I becomes zero when you quotient out by it, so a-b in I means a-b=0 or, written differently, a=b.
 
you would presumably want a equivalent to a, which follows from a-a in I, rather than a+a in I.
 

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