Originally Posted by

**alexandros** .**You are not listening to what i am saying and writing.**

PLease read the whole thread again ,if you are really want to help and not just force your ideas whether wrong or right.

Start with any theorem you like and write a complete proof showing Q' = R,IF YOU wish to do so of course.

Writing parts of the proof make me more confuse.

The versions of the theorem concerning reals and rationals or irrationals that i know are:

1)Given any two girls a<b ,there exist a rational or irrational y, such that: a<y<b

2) Given any real x ,then for any ε>0 there exist a rational or irrational ,y such that

|x-y|<ε.

**None** of them proves that : Q' =R