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Real number proofs

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prove
1 a/b=(ac)/(bc),c can't equal 0

2 a-b < 0, "if and only if" a < b

3 if a < b then -b < -a

4 if 0 < a < b, then (1/b) < (1/a

5 a^2 greater than or equal to 0

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Solution Summary

This provides several proofs of properties of real numbers.

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Proof:
1. Since c is not equal to 0, then for (ac)/(bc), we can cancel out c and get a/b
Thus a/b = (ac)/(bc)
2. "=>" If a - b < 0, then we add b on both sides and get a - b + b < 0 + b, then a < b
"<=" If a < b, then ...

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