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Determine (without proof) the suprema and infima of the following sets: (a) {n € N : n² < 10} (b) {n/(п + m) : т, п€ N} (c) {n/(2n +1) : n € N} (d) {n/m:п, тENwith n +m < 10} Which of the above sets have a maximum? Which have a minimum? (Recall: the notation {x € A : (property of x)} means that the set consists of all of the elements of A that satisfy the property mentioned to the right of the colon, whereas {(expression in x) : x € A} means the set consists of all possible things you get when you plug an element of A into the expression to the left of the colon. Both notations are common all over mathematics. )

Determine (without proof) the suprema and infima of the following sets: (a) {n € N : n² < 10} (b) {n/(п + m) : т, п€ N} (c) {n/(2n +1) : n € N} (d) {n/m:п, тENwith n +m < 10} Which of the above sets have a maximum? Which have a minimum? (Recall: the notation {x € A : (property of x)} means that the set consists of all of the elements of A that satisfy the property mentioned to the right of the colon, whereas {(expression in x) : x € A} means the set consists of all possible things you get when you plug an element of A into the expression to the left of the colon. Both notations are common all over mathematics. )

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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Determine (without proof) the suprema and infima of the following sets: (a) {n € N : n² < 10} (b) {n/(n + m) :т,пEN} (c) {n/(2n+1) : n E N} (d) {n/m:п, тENwith n +m< 10} Which of the above sets have a maximum? Which have a minimum? (Recall: the notation {x € A : (property of x)} means that the set consists of all of the elements of A that satisfy the property mentioned to the right of the colon, whereas {(expression in x) : x € A} means the set consists of all possible things you get when you plug an element of A into the expression to the left of the colon. Both notations are common all over mathematics. )
Transcribed Image Text:Determine (without proof) the suprema and infima of the following sets: (a) {n € N : n² < 10} (b) {n/(n + m) :т,пEN} (c) {n/(2n+1) : n E N} (d) {n/m:п, тENwith n +m< 10} Which of the above sets have a maximum? Which have a minimum? (Recall: the notation {x € A : (property of x)} means that the set consists of all of the elements of A that satisfy the property mentioned to the right of the colon, whereas {(expression in x) : x € A} means the set consists of all possible things you get when you plug an element of A into the expression to the left of the colon. Both notations are common all over mathematics. )
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