"Let I be the set of real numbers that are greater than 0. For each x I, let be the open interval (0,x). Prove that = , = I. For each x I, let be the closed interval [o, x]. Prove that = {0}, = I {0}."
"Let I be the set of real numbers that are greater than 0. For each x I, let be the open interval (0,x). Prove that = , = I. For each x I, let be the closed interval [o, x]. Prove that = {0}, = I {0}."
All of these follow from two basic facts: .
That means that if then .
So . That is the first.
Moreover, for the second: so .
Last edited by Plato; September 30th 2011 at 01:02 PM.