Results 1 to 2 of 2

Thread: irrational numbers

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    1

    irrational numbers

    Can anyone help me with this?
    "if x is an irrational number, is 2x rational or irrational? explain"

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by okami View Post
    Can anyone help me with this?
    "if x is an irrational number, is 2x rational or irrational? explain"

    If $\displaystyle 2x$ were a rational number then there exist integers $\displaystyle a$ and $\displaystyle b$ such that:

    $\displaystyle 2x=\frac{a}{b}$

    but then:

    $\displaystyle x=\frac{a}{2b}$

    but that means $\displaystyle x$ is also rational.

    So if $\displaystyle x$ is irrational $\displaystyle 2x$ must also be irrational as otherwise we have a contradiction (we would have $\displaystyle x$ both rational and irrational and that is not possible).

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Irrational numbers.Why ?
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: Apr 16th 2011, 12:12 PM
  2. Replies: 1
    Last Post: Mar 23rd 2010, 12:55 PM
  3. help on irrational numbers
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Mar 10th 2009, 07:21 AM
  4. Replies: 8
    Last Post: Sep 15th 2008, 04:33 PM
  5. Irrational Numbers
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Sep 15th 2007, 04:15 PM

Search Tags


/mathhelpforum @mathhelpforum