Results 1 to 2 of 2

Math Help - Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite.

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    5

    Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite.

    Well, I can't figure out how to prove this. Just give me hints please

    "Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite."

    Intuitively, a is an element of D is also an assumption. Our Class Reference is the book "Introduction to Advanced Mathematics" by Barnier and Feldman

    Please give me only hints on how to prove this
    Last edited by mr fantastic; October 2nd 2011 at 02:27 AM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Prove: If D is a Dedekind Infinite set then D-{a} is Dedekind infinite.

    One does not need to assume that a ∈ D. If a ∉ D, then D - {a} = D, so it is still Dedekind-infinite.

    Let f : D -> E be a one-to-one correspondence where E is a proper subset of D. Remove f(a) from E.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. e as a Dedekind cut
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 14th 2011, 09:38 PM
  2. Dedekind Cut
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: September 22nd 2010, 08:03 AM
  3. dedekind sets
    Posted in the Advanced Math Topics Forum
    Replies: 6
    Last Post: November 9th 2009, 01:07 PM
  4. sum of two Dedekind cuts
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: August 15th 2009, 03:13 AM
  5. Dedekind Domain
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 26th 2008, 12:39 AM

Search Tags


/mathhelpforum @mathhelpforum