# Thread: Real Numbers Inequality Proof

1. ## 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?

2. 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 $\mathbb{R}$ .