I have to show that two forms of the Archimedean Property are equivalent. The first form is "for every positive real number there is a smaller positive rational number". The second form is that "for every positive real number there is a bigger positive integer".

I tried to show they are equivalent by showing the first implies the second and the second implies the first. However, I am having trouble doing this because one statement involves smaller and the other involves bigger. I would appreciate any hint or suggestion in the right direction.

Thanks