●Let A = [0, 1) and B = [1,2] [1, 2],U then(2 pts) Find sup (An B), sup (A), and sup B

Given that and Now, recall the fact the definition of Supremum.Let (1) (2) For any there exists a…

Answered: ● Let A = [0, 1) and B = [1,2] U [1,2],…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

●
Let A = [0, 1) and B = [1,2] [1, 2],
U then
(2 pts) Find sup (An B), sup (A), and sup B

Expert Solution

Step 1: ''Introduction to solution''

Given that $A equals left square bracket 0 comma 1 right parenthesis space$ and $B equals open square brackets 1 half comma 3 over 4 close square brackets union open square brackets 1 comma 3 over 2 close square brackets$

Now, recall the fact the definition of Supremum.

Let $S u p left parenthesis A right parenthesis equals M$

(1) $x less or equal than M comma space for all x element of A$

(2) For any $epsilon greater than 0 comma space$ there exists a natural number N such that $y greater than open parentheses M minus epsilon close parentheses$

Now, Let Inf $open parentheses A close parentheses equals m$

(1) $m less or equal than x space comma space for all x element of A$

and $for all epsilon greater than 0 comma$ there exists a natural number N such that $y less than left parenthesis m plus epsilon right parenthesis$