Hey, this is the problem
A,B Bounded. Let
I proofed that ( this is false as pointed out by GJA). So by definition bounds . I want to show that indeed by showing that any there's no element in lower than than bounds the set. I trying to make the proof by contradiction, by contradicting the fact that theres a element in etheir set or that bounds it and is lower than its sup.
because of difficulties like these, in defining the real numbers, it is often preferable to define the set of positive real numbers, first. in fact, defining a negative real number is a bit subtle, if one is proceeding by using dedekind cuts.