1. ## Help 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?

2. Originally Posted by calcprincess88
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?

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.

3. If a set is equivelent to any of its proper subsets, then the set is infinite
Hint: Show that $\displaystyle \mathbb{Z}$ is equivalent to $\displaystyle \mathbb{Q}$. Use the Cantors famous diagonal trick. See Proof that rational numbers are countable - from Homeschool Math

4. 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!