Results 1 to 3 of 3

Math Help - Reversing building irrationals on the rationals

  1. #1
    Banned
    Joined
    Oct 2009
    Posts
    769

    Reversing building irrationals on the rationals

    Has anyone tried to start off with irrational numbers as a foundation, then derive the rational numbers from them?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by wonderboy1953 View Post
    Has anyone tried to start off with irrational numbers as a foundation, then derive the rational numbers from them?
    The axiomatic definition of the reals already contains "0", "1", "+" and ".", so the natural numbers can be generated easily from these and the other axioms, once you have the naturals the rationals can be constructed by the usual process.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2009
    Posts
    769
    Quote Originally Posted by CaptainBlack View Post
    The axiomatic definition of the reals already contains "0", "1", "+" and ".", so the natural numbers can be generated easily from these and the other axioms, once you have the naturals the rationals can be constructed by the usual process.

    CB
    It's an interesting fact CB.

    Historically speaking the discovery of the rational numbers preceded the irrational numbers (a secret society was said to have killed someone who revealed the discovery of an irrational number or numbers as that cult feared that the harmony of the rationals would be disrupted). It would seem illogical that the reverse can happen, but to my knowledge nothing has been said about this so I'm exploring this area to see what someone knows about this.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuity question on rationals/irrationals
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 4th 2011, 08:40 AM
  2. Rationals/Irrationals and Continuity
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 27th 2010, 11:03 PM
  3. Rationals and Irrationals
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 8th 2010, 05:32 AM
  4. Function Continuous on Rationals but not on Rationals
    Posted in the Differential Geometry Forum
    Replies: 12
    Last Post: May 28th 2009, 09:49 AM
  5. Proving Irrationals
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 28th 2008, 06:18 PM

Search Tags


/mathhelpforum @mathhelpforum