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Let A=xER: +1} |x | +1 Find inf (A) where A = n Find sup(A). :n,mEN MEN} mws

Let A=xER: +1} |x | +1 Find inf (A) where A = n Find sup(A). :n,mEN MEN} mws

Advanced Engineering Mathematics
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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Please answer both parts of the question. Thanks
E V aragraph > Let A=xER: T 12 N X +1<3) [x] + 1 Normal Find inf (A) where A -|- Find sup(A). 1 No Spac n,mEN
Transcribed Image Text:E V aragraph > Let A=xER: T 12 N X +1<3) [x] + 1 Normal Find inf (A) where A -|- Find sup(A). 1 No Spac n,mEN
Expert Solution
Step 1: Definition of supremum and infimum of a set

Supremum:

Let A be a subset of real numbers.

A real numbe M is said to be supremum of A if

(i) a≤M   ∀a∈A.

(ii) For each ϵ>0 there exists a number aϵ∈A such that M−ϵ<aϵ≤M.

Infimum:

A real number m is said to be an infimum of A if 

(i) a≥m   ∀a∈A.

(ii) For each ϵ>0 there exists a number aϵ∈A such that m≤aϵ<m+ϵ.

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