Results 1 to 2 of 2

Thread: Well-Ordering

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    30

    Well-Ordering

    Prove: If y>0 then there exists a natural number, n, such that n-1 is less than or equal to y < n.

    I'm supposed to prove using the well-ordering property on the set {m as an element of the natural numbers : m > y}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,734
    Thanks
    2810
    Awards
    1
    Quote Originally Posted by GoldendoodleMom View Post
    Prove: If y>0 then there exists a natural number, n, such that n-1 is less than or equal to y < n.
    I'm supposed to prove using the well-ordering property on the set {m as an element of the natural numbers : m > y}
    To use that, you must know that $\displaystyle \mathbb{N}$ is not bounded above.
    Because that is true, $\displaystyle T = \left\{ {m \in \mathbb{N}:y < m} \right\} \ne \emptyset $.
    Every nonempty subset of $\displaystyle \mathbb{N}$ has a first term.
    Let $\displaystyle n = \min \left( T \right) \Rightarrow n \in T \Rightarrow y < n.$
    Moreover, because $\displaystyle n - 1 < n\quad \Rightarrow \quad n - 1 \notin T\quad \Rightarrow \quad n - 1 \leqslant y < n$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with well ordering principle
    Posted in the Discrete Math Forum
    Replies: 17
    Last Post: May 23rd 2011, 02:40 PM
  2. Well Ordering
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: Sep 8th 2010, 04:04 AM
  3. well ordering principle
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Aug 18th 2009, 02:18 PM
  4. well-ordering
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Jun 10th 2009, 10:24 AM
  5. well ordering
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Jul 17th 2008, 10:16 AM

Search Tags


/mathhelpforum @mathhelpforum