# Real Numbers Inequality Proof

• March 30th 2011, 12:03 AM
jstarks44444
Real Numbers Inequality Proof
Let x,y be elements of the Real Numbers such that x < y. There exists z in the Real Numbers such that x < z < y.

Any thoughts on this proof?
• March 30th 2011, 01:28 AM
FernandoRevilla
Quote:

Originally Posted by jstarks44444
Let x,y be elements of the Real Numbers such that x < y. There exists z in the Real Numbers such that x < z < y.

Choose $z=(1/2)(x+y)$ and use the standard arithmetic and ordering axioms of $\mathbb{R}$ .