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Math Help - inequality proof

  1. #1
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    inequality proof

    1) Let a,b,c e Z. If a < b, then a + c < b + c.

    2) Let a,b,c e Z. If a < b and b < c, then a < c.

    ANy advice?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jzellt View Post
    1) Let a,b,c e Z. If a < b, then a + c < b + c.
    why not just start with a < b and then add c to both sides?

    2) Let a,b,c e Z. If a < b and b < c, then a < c.

    ANy advice?
    i'm not sure what you want here. these seem pretty straight forward. we have a < b < c. it follows by the transitivity of "<" that a < c.

    if you want to do it more flashy, perhaps...

    assume a < b and b < c. from a < b we have a - b < 0. but a - c < a - b since b < c. but that means we have a - c < 0 by transitivity of "<". now add c to both sides.


    in any case, you would do well to tell us what axioms you have to work with
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