How to compare sums of infimum (or supremum) of two sets?

Asked Jul 12 '17 at 07:00

Active Jul 12 '17 at 08:28

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Which of this expression are correct ? Why or why not ? How can check it by myself?

edited Jul 12 '17 at 08:28

asked Jul 12 '17 at 07:00

faoxis

2

$x_n+y_n\le \sup{x_n}+\sup{y_n}\implies \sup{x_n+y_n}\le \sup{x_n}+\sup{y_n}$ – mfl Jul 12 '17 at 07:02
@mfl why $ => $ ? – faoxis Jul 12 '17 at 08:25
1

Because $\sup{x_n}+\sup{y_n}$ is an upper bound. – mfl Jul 12 '17 at 13:17
Got it. Thanks! – faoxis Jul 13 '17 at 07:24

0 Answers0