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Math Help - Analysis order question

  1. #1
    Junior Member
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    Aberystwyth, Wales
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    Analysis order question

    I'm reading though my analysis book and a came across this it says the following is true
    (∀n∈N)(∃m∈N) m>n
    which i understand but the follow is not:
    (∃m∈N)(∀n∈N) m>n

    which i dont get at all they both seem true to me. Could someone explain please
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  2. #2
    Senior Member Tinyboss's Avatar
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    Just read them aloud. The first says, "for any n, there exists an m such that m>n", i.e. for every number there's a bigger number, clearly true.

    The second says, "There exists an m, such that for any n, m>n", i.e. there's a number that's bigger than every other number, clearly false.
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