Find the sup, inf, max, and min of each set, if it exists. Prove that your answers arecorrect.For example, it might look like:Theorem: Let S = {...}. Then sup S = max S = 4, inf S =-, and S has no min.You then need to prove that sup S = max S = 4, that inf S = -, and that S has nomin.(a) A = [2,8) = {r € R: 2

We find sup and inf of given set

orrect. or example, it might look like: 'heorem: Let S = {...}. Then sup S = max S = 4, inf S = -, and S has no min. ou then need to prove that sup S = max S = 4, that inf S = -, and that S has no ain. a) A = [2,8) = {r ER:2

orrect. or example, it might look like: 'heorem: Let S = {...}. Then sup S = max S = 4, inf S = -, and S has no min. ou then need to prove that sup S = max S = 4, that inf S = -, and that S has no ain. a) A = [2,8) = {r ER:2

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 1TFE: Label each of the following statements as either true or false. 1. , for every nonempty set A.

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Question

Find the sup, inf, max, and min of each set, if it exists. Prove that your answers are
correct.
For example, it might look like:
Theorem: Let S = {...}. Then sup S = max S = 4, inf S =-, and S has no min.
You then need to prove that sup S = max S = 4, that inf S = -, and that S has no
min.
(a) A = [2,8) = {r € R: 2<r< 8}
(b) В —
S 1
:neN
S(-1)"
(c) C =
:n €N
(You may use without proof the fact that (-1)" is -1 if n is odd and 1 if
n is even.)
Sn+2
In? +1
(d) Đ =
:nEN

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