I need help with this question. It says to use Corollary 5.10(meaning this: A finite set is not equivalent to any of its proper subsets) to show that the rationals Q are infinite.

How would I go about doing this?

Thanks for your help!

Printable View

- Apr 25th 2008, 06:34 PMcalcprincess88Help with a proof please!
I need help with this question. It says to use Corollary 5.10(meaning this: A finite set is not equivalent to any of its proper subsets) to show that the rationals Q are infinite.

How would I go about doing this?

Thanks for your help! - Apr 25th 2008, 08:46 PMTheEmptySet
Lets rewrite the Corollary as an if then statement

If a Set is finite then it is not equivelent to any of its proper subsets

$\displaystyle p \implies q$

Use the contrapositive of this corollary.

$\displaystyle \sim q \implies \sim p$

if a set is equivelent to any of its proper subsets, then the set is infinite

See what you can do from here.

Good luck. - Apr 25th 2008, 09:59 PMIsomorphismQuote:

If a set is equivelent to any of its proper subsets, then the set is infinite

- Apr 27th 2008, 11:07 AMcalcprincess88
Thanks for your help! I'll try to do it and see what I can come up with and if I need anymore help I'll come back! Thanks again!