1. ## Real Analysis Proof

Prove that if x is in set Q (all rational numbers), y is in set Q and x < y, then there is some z in set Q such that x < z < y.

It is certain that if x<y then x cannot be greater than or equal to y.. also z can between x and y because there can be repeating decimals, and say x is 4 and y is 4.1, then there must always be a z that is in between these numbers... even if its 4.09999999999999 (repeating). I don't know how to write this in the form of a proof. Can anyone help?

2. OH! Come on will you.
$a < b\, \Rightarrow \,a < \frac{{a + b}}{2} < b$
That is true for all real numbers $a\;\&\;b$.