Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By Plato

Math Help - Real analysis

  1. #1
    Newbie
    Joined
    Jun 2013
    From
    Nigeria
    Posts
    1

    Real analysis

    P/s i need help to prove that every positive real no has a unigue positive square root
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1477
    Awards
    1

    Re: Real analysis

    Quote Originally Posted by Mondella View Post
    P/s i need help to prove that every positive real no has a unigue positive square root
    Any proof of this depends upon the set of definitions and axioms with the sequence of theorems you have.

    Here is a general approach. If c\in\mathbb{R}^+ prove that if 0<t~\&~t^2=c then there is at most one such t.
    Let E=\{x\in\mathbb{R}^+:x^2<c\}. You want to show that E\ne\emptyset and E is bounded above.
    If you can show those then use the completeness property.

    Hint: let t=\frac{c}{1+c}. Is it true that t\in E~?

    What can you do with that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    From
    Minnesota
    Posts
    80
    Thanks
    8

    Re: Real analysis

    Plato, can you explain why this doesn't work? Given distinct real numbers x and y in R, suppose they have the same square root z. By definition, z = sqrt(x) and z=sqrt(y), so we have z^2=x=y which is a contradiction, so two distinct real numbers can not have the same square root.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1477
    Awards
    1

    Re: Real analysis

    Quote Originally Posted by Lord Voldemort View Post
    Plato, can you explain why this doesn't work? Given distinct real numbers x and y in R, suppose they have the same square root z. By definition, z = sqrt(x) and z=sqrt(y), so we have z^2=x=y which is a contradiction, so two distinct real numbers can not have the same square root.
    How do does that prove that if x\in\mathbb{R}^+ that \sqrt{x} exists at all?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. real analysis
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: August 18th 2009, 12:32 AM
  2. Real Analysis....Any Help??
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 04:02 PM
  3. Real Analysis
    Posted in the Calculus Forum
    Replies: 12
    Last Post: February 18th 2009, 05:32 PM
  4. Real Analysis Help!!
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 6th 2008, 06:38 PM
  5. real analysis
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 4th 2007, 08:58 PM

Search Tags


/mathhelpforum @mathhelpforum