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    using proof by contradiction, show that there are an infinte number of rational numbers between 0 and 1.

    I can never do these...is there a standard method to follow?
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    (Original post by hohum)
    using proof by contradiction, show that there are an infinte number of rational numbers between 0 and 1.

    I can never do these...is there a standard method to follow?
    This is one of those a/b things int it?!? :confused:
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    (Original post by hohum)
    using proof by contradiction, show that there are an infinte number of rational numbers between 0 and 1.

    I can never do these...is there a standard method to follow?
    If there isn't an infinite amount, say there are n rational numbers, with m/n the highest, where 0<n and 0<m, and n>m. But consider (m+1)/(n+1), this is another larger rational number between 0 and 1, so contradiction.
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    (Original post by mik1a)
    If there isn't an infinite amount, say there are n rational numbers, with m/n the highest, where 0<n and 0<m, and n>m. But consider (m+1)/(n+1), this is another larger rational number between 0 and 1, so contradiction.
    surely assume there are a finite number between 0 and 1 namely
    a1, a2, a3......1

    ok but wot does (a1+a2)/2=???x??
    we have new one
    and wot about (a1+x)/2=


    so we have a contradiction
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    Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
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    can you say:

    assume there is a finite number blah...

    n / n+1 where n can take any +ve integer

    therefore there is a finite number of rational numbers as n is infinite itself

    ????????
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    (Original post by rae)
    can you say:

    assume there is a finite number blah...

    n / n+1 where n can take any +ve integer

    therefore there is a finite number of rational numbers as n is infinite itself

    ????????
    Oh great you're all stupidly clever compared to me! Thanks though, I see your thinking even if I can't think it myself!
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    (Original post by Jonny W)
    Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
    that's a nice one. I like that one.
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    (Original post by Jonny W)
    Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
    Or of course the opposite. let x be the greatest rational number between 0 and 1 (non inclusive) x^2 is a bigger rational number! I know the proble has beeen solved but I thought i'd put in my two pence

    MB
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    (Original post by musicboy)
    Or of course the opposite. let x be the greatest rational number between 0 and 1 (non inclusive) x^2 is a bigger rational number! I know the proble has beeen solved but I thought i'd put in my two pence
    x^2 < x, so your proof isn't the opposite.
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    (Original post by Jonny W)
    x^2 < x, so your proof isn't the opposite.
    In fact its not even a proof. Surely it should be if x is the greatest rational number with 0<x<1, then what is (x+1)/2 ? Well its greater then x , contradiction
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    (Original post by Jonny W)
    (Original post by musicboy)
    Or of course the opposite. let x be the greatest rational number between 0 and 1 (non inclusive) x^2 is a bigger rational number! I know the proble has beeen solved but I thought i'd put in my two pence

    MB
    x^2 < x, so your proof isn't the opposite.
    can't you call x the lowest rational number instead? then x^2 is lower...
 
 
 
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