Which of the following sets have a supremum in R?{ZEQ: 0≤z <√√√2}{z² – 1: z € Z}-(2² – 32² +2:{z²3: ZEN}{ZER: 0≤z≤ √√2}Drag answer hereDrag answer hereDrag answer hereDrag answer hereDoes not havesupremumHas supremum

Which of the following sets have a supremum in ?1. 2. 3. 4.

Answered: Which of the following sets have a…

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

Which of the following sets have a supremum in R?
{ZEQ: 0≤z <√√√2}
{z² – 1: z € Z}
-
(2² – 32² +2:
{z²
3
: ZEN}
{ZER: 0≤z≤ √√2}
Drag answer here
Drag answer here
Drag answer here
Drag answer here
Does not have
supremum
Has supremum

Expert Solution

Step 1: Question Description

Which of the following sets have a supremum in $straight real numbers$ ?

1. $open curly brackets z element of straight rational numbers space colon space 0 less or equal than z less or equal than square root of 2 close curly brackets$

2. $open curly brackets z squared minus 1 space colon space z element of straight integer numbers close curly brackets$

3. $open curly brackets z squared minus fraction numerator 3 z squared plus z over denominator 3 end fraction space colon space z element of straight natural numbers close curly brackets$

4. $open curly brackets z element of straight real numbers space colon space 0 less or equal than z less or equal than square root of 2 close curly brackets$

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Which of the following sets have a supremum in R? {ZEQ:0≤z ≤ √2} {z²-1: ze Z} {z² - 3z²+z 3 : ZEN} {ZER:0 ≤z≤ √2} Drag answer here Drag answer here Drag answer here Drag answer here Does not have supremum Has supremum