1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Well-Ordering Principle on Natural Numbers

  1. Jan 13, 2012 #1
    This is my first proof and post. I'll eventually get better at tex.

    1. The problem statement, all variables and given/known data

    If [itex] n \in N[/itex], then [itex]n ≥ 0[/itex].

    Hint: [itex]N \subset N[/itex] (thus not any empty set) and has least member by the well-ordering principle.

    2. Relevant

    (i) [itex]0 \subset N[/itex]

    (ii) [itex]n+1 \in N[/itex] for all [itex] n \in N[/itex]

    (iii) [itex]n-1 \in N [/itex]for all [itex] n \in N [/itex]such that n≠0

    (iv) The well-ordering principle itself.

    3. The attempt at a solution

    As the hint suggests, I am supposed to prove this using the well-ordering principle.

    [itex]n-1 \in N[/itex] for all [itex] n \in N[/itex] such that n≠0. [itex] N \subset N[/itex] so N≠∅ and has a least member by well-ordering principle.

    I used (iii) [itex] n-1 \in N [/itex] for all n in N such that n≠0. But

    [itex](n=0) \in N[/itex] and [itex]-1 \notin N[/itex]. Hence, [itex] -1<n → 0≤n[/itex]

    I'm not sure if this is right though.

    Additionally, is there any way to write text inbetween {itex} text {/itex} such that notations appear in addition to original text?
    Last edited: Jan 13, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted