# Real number proofs

-(-a)=a

-(a)*-(b)=a*b

if a doesn't equal 0 then 1/a doesn't equal 0

if a doesn't equal 0 then (-1)/a = 1/(-a)

a(b-c)=ab-ac

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#### Solution Preview

Proof:

1. Since a + (-a) = 0, then we subtract (-a) on both sides and get

a = 0 - (-a).

So we get -(-a) = a

2. Since -(a) = (-a), then we use the result in 1 and get

-(a) * -(b) = (-a) * -(b) = -(-a) * b = a * b

...

#### Solution Summary

This provides examples of proving several properties of real numbers.

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