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Math Help - Archimedean property help

  1. #1
    Senior Member Danneedshelp's Avatar
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    Archimedean property help

    Q: If y is in R, y>0, then there is a positive integer n such that 1/n<y.

    A: All I can think of is to use the fact that N is unbounded, thus for any value of y I can creat a smaller fraction with a larger value of n.

    Also,

    Q: Consider the set A={1/n : n is in R}. Prove that inf(A)=0.

    Any help understanding how to do these would be much appreciated. Thank you.
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  2. #2
    Super Member
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    Quote Originally Posted by Danneedshelp View Post
    Q: If y is in R, y>0, then there is a positive integer n such that 1/n<y.

    A: All I can think of is to use the fact that N is unbounded, thus for any value of y I can creat a smaller fraction with a larger value of n.
    Try and be a bit more formal here.

    Suppose  \exists \ y \in \mathbb{R} \ y>0 \  | \ \forall \ n \in \mathbb{N} \  \frac{1}{n} > y \ \implies \  \frac{1}{y} > n \  \forall  \ n \in \mathbb{N}  then some comment about the contradiction there would be nice.

    Bobak
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