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. )

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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