Originally Posted by

**Hartlw** I thought it was clear throughout the discussion that we were talking Archimedes Classic Math Postulate (Principle, Theorem) as stated in my first post or, for example, Birkhoff and McLean, and as responded to by most participants. This thread was started by suggesting it was a paradox. But I relented and posted:

"How about we conclude that N > r for all r not because integer N is unbounded (so is r), but because of a primal property of integers that every integer has a larger integer. Works for me. (Archimedes Postulate is OK) "

If you wish to start (why at this point) a new topic about some abstract version, I suggest a new thread appropriateley titled for those interested.

EDIT To repeat: Archimedes Postulate: For any real number r an integer N exists st N > r. What is your version?