1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Are the following statements all equivalent?

  1. Oct 11, 2013 #1
    1) Peano axioms for the natural numbers
    2) Well-ordering principle
    3) Principle of mathematical induction
    4) Principle of complete induction

    Are they all equivalent? I'm going to attempt to prove them if they are, but I'd like someone to point out whether they are or not. I've heard that they are but I may be wrong. Thanks!

  2. jcsd
  3. Oct 11, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    All statements are equivalent for a given definition of "equivalent". :D
    You may find that some of them are consequences of another with some extra restrictions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Are the following statements all equivalent?
  1. Equivalent Statements (Replies: 3)