Proving an irrational number exists in the interval (x/t, y/t)

[cpl1992]

Homework Statement

Let x,y,t be in the set of all real numbers (R) such that x<y and t>0. Prove that there exists a K in the set of irrational numbers (R\Q) such that x<(K/t)<y

Homework Equations

if x,y are in R and x<y then there exists an r in Q such that x<=r<y

The Attempt at a Solution

0<x<y implies that 0<(1/y)<(1/x)

 

[jbunniii]

Hint: if you choose some specific irrational such as $\sqrt{2}$, then the sum of this number plus any rational is irrational.