Hey all,

(this is my first post so bear with me haha)

I have to use the Archimedean principle (For every real number x, there is an integer n such that n > x) to prove this:

For every positive real number q, there is a positive integer N such that 1/n < q for every integer n >= N.

Now, my response to this was:

Because of the Archimedean Principle, there will always be an n greater than q. Thus when n >= N, 1/n < q because as n gets larger, it will reach infinity, and approach 0. Since q > 0, and n > q, 1/n < q.

Did I do this right? If not, how can I prove this with the AP? Thanks for the help!