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Math Help - rational numbers proof

  1. #1
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    rational numbers proof

    Let  a,b \epsilon R, with  a<b . Show that there exists a number  x\epsilon R such that  a<x<b, with  x rational or not rational, as we wish.

    Thank you!!!!
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    Quote Originally Posted by Barton View Post
    Let  a,b \epsilon R, with  a<b . Show that there exists a number  x\epsilon R such that  a<x<b, with  x rational or not rational, as we wish.

    Thank you!!!!
    Choose
    x = \frac{a + b}{2}

    I leave it to you to show that x has the required property.

    -Dan
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