Results 1 to 2 of 2

Math Help - Real Analysis

  1. #1
    Newbie
    Joined
    Aug 2013
    From
    europe
    Posts
    1

    Real Analysis

    I need to prove the following statements:


    • Prove that if f: [a, b] -> R is equal to zero on every rational number in [0,1] and it's continuous then f(x)= 0 for any x that belongs to [a, b] .


    and


    • Proof that in a normed vector space the convex hull of a compact set is compact
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    606
    Thanks
    168

    Re: Real Analysis

    If there existed an irrational t number such that f(t) was not equal to 0 then f(x) would not be continuous, there would be a sharp change in f(x) from 0 to f(t) to 0.
    Try to express that formally in mathematics
    It might help to know that there is an irrational number between every two rational numbers and vice versa.
    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: September 12th 2009, 02:37 PM
  2. Real Analysis
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 27th 2009, 07:02 AM
  3. Real analysis
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 13th 2009, 10:47 AM
  4. Real Analysis
    Posted in the Calculus Forum
    Replies: 12
    Last Post: February 18th 2009, 06:32 PM
  5. real analysis
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 4th 2007, 09:58 PM

Search Tags


/mathhelpforum @mathhelpforum