Cardinality and Counting

  • Thread starter dabdobber
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  • #1
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Main Question or Discussion Point

I need help with this math problem:

Show that the set of rational numbers, Q, is countable.

and

Show that the set of irrational numbers is uncountable.
 

Answers and Replies

  • #2
22,097
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What do you know about cardinality already? Are there any theorems you've seen that might be useful?
What did you try already??
 
  • #3
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well as far as the first one goes I know that the set of integers Z is a subset of Q and that Z is countable. now I make B as the set of all non-integral rational numbers.

if B is countable, then Q is countable because a union of two countable sets is countable.
thats my approach, but i'm not much of an example person.

and for the second one i'm thinking that I can show the union of the reals IR with the irrational, thus making them uncountable as well?
 
  • #4
lanedance
Homework Helper
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1) try and set up a 1:1 map between Q and Z
2) show that no such map exists for R-Q
 

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