1. Let U = (3,7]. a. Prove that 7.1 is not the least upper bound for U. b. Prove that 6.9 is not the least upper bound for U. c. Prove that 7 is the least upper bound for U.

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help pls proofs

1. Let U = (3,7].
a. Prove that 7.1 is not the least upper bound for U.
b. Prove that 6.9 is not the least upper bound for U.
c. Prove that 7 is the least upper bound for U.
2. Let U = (3,7].
%3D
a. Prove that 3.1 is not the greatest lower bound for U.
b. Prove that 2.9 is not the greatest lower bound for U.
c. Prove that 3 is the greatest lower bound for U.
4. Find find the glb and lub of W = [5,6) and prove your answers are correct.
%3D
5. Find the glb of Z=[5, infinity) and show that there is no upper bound.
6. Find find the glb and lub of V = {1-(1/n) | n is a natural number} and prove your answers are correct.
%3D
Transcribed Image Text:1. Let U = (3,7]. a. Prove that 7.1 is not the least upper bound for U. b. Prove that 6.9 is not the least upper bound for U. c. Prove that 7 is the least upper bound for U. 2. Let U = (3,7]. %3D a. Prove that 3.1 is not the greatest lower bound for U. b. Prove that 2.9 is not the greatest lower bound for U. c. Prove that 3 is the greatest lower bound for U. 4. Find find the glb and lub of W = [5,6) and prove your answers are correct. %3D 5. Find the glb of Z=[5, infinity) and show that there is no upper bound. 6. Find find the glb and lub of V = {1-(1/n) | n is a natural number} and prove your answers are correct. %3D
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