REAL ANALYSIS I Prove the following exercises (please show all your work)- Exercise 1.1.2: Let S...

REAL ANALYSIS I

Prove the following exercises (please show all your work)-

Exercise 1.1.2: Let S be an ordered set. Let A ⊂ S be a nonempty finite subset. Then A is bounded. Furthermore, inf A exists and is in A and sup A exists and is in A. Hint: Use induction.

Exercise 1.1.9: Let S be an ordered set and A is a nonempty subset such that sup A exists. Suppose there is a B ⊂ A such that whenever x ∈ A there is a y ∈ B such that x ≤ y. Show that sup B exists and sup B = sup A.

Expert Solution

Colby Messinger answered 2 years ago

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