Hi, I have the following three problems, but I only want to know what the first one is like... I am sure I will then be able to figure out the other two.
The problem says:
"In the following, a, b are real numbers.
1) Let b>a+1. Show that there is an integer m such that a<m<b.
2) Let a,b > 0. Show that there is an integer n such that n*a > b.
3) Let a<b. Prove that there is an integer n such that n*b > n*a+1. Conclude that there is a rational number q such that a<q<b."
I would really appreciate it if you could give me a hand with the first one so that I can see how to solve the other 2 problems. Thanks a lot!