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Math Help - [SOLVED] Is this irrationnal ? Rationnal ? Or rationnaly interesting ?

  1. #1
    Moo
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    [SOLVED] Is this irrationnal ? Rationnal ? Or rationnaly interesting ?

    Hello !

    Here is a little problem :

    Proove that there exists two irrationnals a & b such as a^b is a rationnal.

    The proof is very easy, but you have to know it
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  2. #2
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    I know what you are looking for. But I have a different solution. e^{\ln 2} = 2.
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  3. #3
    Moo
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    This is good too

    Erm...is ln(2) irrationnal ?

    I love the demo i read, because it's like...juggling with maths hihi
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    Behold, the power of SARDINES!
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    \left( 2^\pi\right)^\frac{1}{\pi}
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    Moo
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    Yes, this is the kind of demo it was given ^^

    ((\sqrt{2})^{\sqrt{2}})^{\sqrt{2}}
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Moo View Post
    This is good too

    Erm...is ln(2) irrationnal ?

    I love the demo i read, because it's like...juggling with maths hihi
    Suppose otherwise, then there exist integers a and b such that e^{a/b}=2.

    Then:

    e=\root a \of{2^b}

    Now the left hand side is transcendental and the right hand side algebraic - a contradiction.

    RonL
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