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Proof about less than

  1. Jan 24, 2014 #1
    1. The problem statement, all variables and given/known data
    prove that if a; b; c are natural
    numbers and if a < b and b < c, then a < c.

    Some axioms we are allowed to use is if a<b then there exists a natural number e
    such that a+e=b.
    3. The attempt at a solution
    If a<b then there is a natural number x such that a+x=b,
    if b<c then there exists a natural number y such that b+y=c,
    Now since b= a+x then a+x+y=c and since x+y is a another natural number, call it z then
    a+z=c which implies a<c.
    Is this the correct way to go about it.
     
  2. jcsd
  3. Jan 24, 2014 #2

    maajdl

    User Avatar
    Gold Member

    Right.
     
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