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ssayan3
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Least Upper Bound proof...
Suppose A is a nonempty set that has x as an upper bound. Prove that x is the least upper bound of the set A iff for any E>0 there exists a y in A such that y>x-E
None
The forward where you assume that x is the least upper bound is very easy, but I'm having some trouble proving the reverse...
This is what I have so far...
Let x be an upper bound of A, and choose a point z in A.
If x is an upper bound of A, then x+z is also an upper bound.
Homework Statement
Suppose A is a nonempty set that has x as an upper bound. Prove that x is the least upper bound of the set A iff for any E>0 there exists a y in A such that y>x-E
Homework Equations
None
The Attempt at a Solution
The forward where you assume that x is the least upper bound is very easy, but I'm having some trouble proving the reverse...
This is what I have so far...
Let x be an upper bound of A, and choose a point z in A.
If x is an upper bound of A, then x+z is also an upper bound.