# Thread: Proof...did I do it?

1. ## Proof...did I do it?

Here I go again with these proofs, this time I am trying to prove the sum of two rational numbers is rational.

This is what I have...

Assume x is rational
Assume y is rational
Let x=a/b where a and b are integers and b does not equal 0
Let y=c/d where c and d are integers and d does not equal 0
Let v=bd
We check that w and v are integers which they are and the integers are closed under addition and multiplication
Therefore the sum of two rational numbers is rational

2. I'm guessing you're allowed to assume that the product of two integers is still an integer. Then you can indeed say that $\displaystyle \frac{ad+ bc}{bd}$ is a rational number, i.e. the ratio of two integers.

3. Originally Posted by o_O
I'm guessing you're allowed to assume that the product of two integers is still an integer. Then you can indeed say that $\displaystyle \frac{ad+ bc}{bd}$ is a rational number, i.e. the ratio of two integers.
Well, he noted that $\displaystyle \mathbb{Z}$ is closed under multiplication, so that seems to be the case.

Nice work, sjenkins!

4. Thanks so much! Finally, I got one!!!!