- #1
dancergirlie
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Homework Statement
Use the completeness axiom to prove that to prove that every non-empty subset of real numbers, which is bounded below, has a greatest lower bound.
Homework Equations
N/A
The Attempt at a Solution
Assume A is a nonempty subset of real numbers which is bounded below. Define B as the set of of lower bounds for A, meaning for all b in B, b is less than or equal to all a in A. Since every element in A is greater than every element in B, A is the set of upper bounds for B. According to the completeness axiom, every non-empty set of real numbers that is bounded above has a least upper bound, which would mean that the B is bounded above and SupB is an element in A.
**This is where i get stuck. I need to show that the SupB=InfA, which would mean that the element is in both sets**
Any help/tips would be greatly appreciated :)