Results 1 to 5 of 5

Math Help - 2 exercises

  1. #1
    Member SENTINEL4's Avatar
    Joined
    Mar 2009
    From
    Kastoria, Greece
    Posts
    92

    2 exercises

    1) { r_{n}}=Q , E={x \inX : g(x)<f(x)}
    Show that E= \bigcup_{r_{n}}[{x \inX : g(x)< r_{n}} \bigcap{x \inX : f(x)> r_{n}}]


    2) {x \inX : g(x)+f(x)<a} = {x \inX : g(x)<a-f(x)}.
    If f(x) is a countable function show that a-f(x) is countable function too.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by SENTINEL4 View Post
    1) { r_{n}}=Q , E={x \inX : g(x)<f(x)}
    Show that E= \bigcup_{r_{n}}[{x \inX : g(x)< r_{n}} \bigcap{x \inX : f(x)> r_{n}}]


    2) {x \inX : g(x)+f(x)<a} = {x \inX : g(x)<a-f(x)}.
    If f(x) is a countable function show that a-f(x) is countable function too.
    Before spending time on this please make sure this is what you mean.
    E = \bigcup\limits_n {\left[ {\left\{ {x \in X:g(x) < r_n } \right\} \cap \left\{ {x \in X:f(x) > r_n } \right\}} \right]}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,963
    Thanks
    1631
    Also, what do you mean by "countable function"? I know what "countable sets" are but not "countable function". It may be a translation problem. Do you mean "measurable function".
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member SENTINEL4's Avatar
    Joined
    Mar 2009
    From
    Kastoria, Greece
    Posts
    92
    @Plato
    Under the \bigcup is r_{n} not n.

    @HallsofIvy
    It means measurable not countable.
    Last edited by Plato; May 12th 2009 at 12:39 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    y \in E\; \Rightarrow \;g(y) < f(y)\; \Rightarrow \;\left( {\exists j} \right)\left[ {r_j  \in \mathbb{Q} \wedge g(y) < r_j  < f(y)} \right]
    \; \Rightarrow \;y \in \left\{ {x \in X:g(x) < r_j } \right\} \cap \left\{ {x \in X:f(x) > r_j } \right\}


    \begin{gathered}<br />
  z \in \bigcup\limits_n {\left[ {\left\{ {x \in X:g(x) < r_n } \right\} \cap \left\{ {x \in X:f(x) > r_n } \right\}} \right]}  \hfill \\<br />
  \left( {\exists k} \right)\left[ {z \in \left\{ {x \in X:g(x) < r_k } \right\} \cap \left\{ {x \in X:f(x) > r_k } \right\}} \right] \hfill \\<br />
  \; \Rightarrow \;g(z) < r_k  < f(z)\; \Rightarrow \;z \in E \hfill \\ <br />
\end{gathered}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exercises (functions )
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 13th 2010, 11:08 AM
  2. Some exercises
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: March 30th 2010, 07:32 AM
  3. Please help me with these exercises!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 7th 2009, 08:24 AM
  4. Need help with few exercises. Please help!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 26th 2009, 01:10 AM
  5. please help me with these exercises
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 19th 2008, 12:48 PM

Search Tags


/mathhelpforum @mathhelpforum