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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

    © BrainMass Inc. brainmass.com October 9, 2019, 10:23 pm ad1c9bdddf
    https://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.

    $2.19