Homework Help: I need help solving a proof dealing with the set of irrational numbers.

1. Oct 4, 2012

cpl1992

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. The attempt at a solution
0<x<y implies that 0<(1/y)<(1/x)

2. Oct 4, 2012

jbunniii

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