# Real number proofs

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

© BrainMass Inc. brainmass.com October 9, 2019, 10:23 pm ad1c9bdddfhttps://brainmass.com/math/discrete-math/real-number-proofs-218871

#### Solution Preview

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 ...

#### Solution Summary

This provides several proofs of properties of real numbers.

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