Archimedean property of R proof

[missavvy]

Homework Statement

Using the density of Q(rationals) in R(real numbers), prove the Archimedean property.

Homework Equations

Density of Q in R: For all x,y in R, and x<y, there exists q in Q s/t x<q<y.
Archimedean property says: For every real number x there exists a natural number y such that y>x.

The Attempt at a Solution

So I know how to prove the density of Q in R using the Archimedean property but I'm not sure of how to do it the other way around. Also, I don't really understand why it makes sense to prove it the other way around? Any hints and explanations would be helpful! thanks

 

[╔(σ_σ)╝]

The problem does seem that hard. If x is negative y can be 1. If x is positive you know that

x< q < x+1

where q is a positive rational

or
x< q = s/t

Remember what a rational number is ,that is, s and t are integers. You may also have to assume that s and t have no common factors eg we write 3/2 not -3/-2 :-).