Results 1 to 5 of 5

Math Help - [SOLVED] relation question

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    112

    Exclamation [SOLVED] relation question

    I think this goes here.

    a  \epsilon  \mathbb{R} \text{ and }0<a<1 \Rightarrow<br />
0<1-\sqrt{1-a}<a

    I'm not sure where to start with this proof, rather i'm not sure where to start with this proof if I do not use the fact that I can square both sides.

    because I think: {a^2}<{1^2}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    If 0<x<1 then \sqrt x > x.

    Now 0<1-a<1, hence \sqrt{1-a}>1-a and you have it.

    (Note that in LaTeX, \in = \in and \epsilon = \epsilon)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    112
    It took me a while to figure out the latex thing i've never used it before.

    Though I'm not sure I'm allowed this fact
    \sqrt x > x for |x|<1

    I know I'm allowed to use:

    a<b \text{ and } b<c \Rightarrow a<c

    a<b \text{ and } c\in \mathbb{R} \Rightarrow a+c < b+c

    a<b \text{ and } c>0 \Rightarrow ac<bc<br />

    So I guess in essence I need to prove for 0<x<1\text{  }\sqrt x > x
    Last edited by seld; September 8th 2009 at 08:17 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    You have x<1. Multiply by x on both sides and you have x^2<x. Take the square root on both sides and you have x<\sqrt x.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2009
    Posts
    112
    thank you for both help with this and the latex
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Equivalence Relation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 29th 2010, 02:41 PM
  2. [SOLVED] Transitive relation help please?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 23rd 2010, 01:39 AM
  3. [SOLVED] Equivalence relation proof?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 22nd 2010, 12:09 PM
  4. [SOLVED] equivalence relation/classes question.
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: July 28th 2009, 03:44 PM
  5. [SOLVED] recurrence relation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 12th 2008, 09:13 PM

Search Tags


/mathhelpforum @mathhelpforum