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Math Help - Finite, countably infinite, or uncountable

  1. #1
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    Finite, countably infinite, or uncountable

    Determine, with justification, whether each of the following sets is finite, countably infinite, or uncountable.

    a) {  x \in Q | 1 < x < 2 }

    b) {  m/n  |  m, n \in N, m < 100, 5 < n < 105 }


    I am lost. Not sure how to approach these problems!

    Thanks.
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  2. #2
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    Quote Originally Posted by JohnM25 View Post
    Determine, with justification, whether each of the following sets is finite, countably infinite, or uncountable.
    a) {  x \in Q | 1 < x < 2 }

    b) {  m/n  |  m, n \in N, m < 100, 5 < n < 105 }
    For part a) A subset of a countable set is countable. Is it infinite?

    Part b) is unreadable.
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  3. #3
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    part b) given that the possible values of m (let's call this set A) are finite in number, and likewise for the possible values of n (call this set B), can you see that your set is smaller than AxB?

    what can you say about the size of AxB when A and B are finite? can you think of a way to map AxB to your set that is onto, proving that your set MUST be smaller?
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