- #1

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

and

Show that the set of irrational numbers is uncountable.

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- Thread starter dabdobber
- Start date

- #1

- 2

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

and

Show that the set of irrational numbers is uncountable.

- #2

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What did you try already??

- #3

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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

2) show that no such map exists for R-Q

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