- #1
jaqueh
- 57
- 0
Homework Statement
Prove that for every a in ℝ, and the set E = {rεQ : r<a}
the following equality holds:
a = sup(E)
The Attempt at a Solution
I'm not sure where to go? should i do this by contradiction that a≠sup(e) or should i do a traditional supremum proof or should i even do an epsilon proof?
I have let x be an element of R then E is the set {r element Q : r<x}. MY QUESTION is how do I say that x is the greatest number of the set?
do i do:
case 1: y is an element of E such that y=x, then x is a rational
case 2: y is an element of E such that y<x, then x is irrational?
Last edited: