1. ## prove or disprove

for all x,y in Real Number , that x > y , then there exists a number Z , such that x<z and z < y.

I concluded this is a false statement because the inequality would be Z > x > y > Z which make no sense, but how to disprove this?.

2. ## Re: prove or disprove

assume x > y, z > x and z < y,

if x > y then x - y >0,

since z < y then z - y < 0 < x - y so z - y < x - y and so z < x but we assumed z > x which is a contradiction