AnalysisHW2 125A

AnalysisHW2 125A - MAT 125a, HW2 Solutions 7 (a) (max { a,b...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAT 125a, HW2 Solutions 7 (a) (max { a,b } = a + b + | a- b | 2 ): There are two cases: a b and a < b . If a b then we have a + b + | a- b | 2 = a + b + a- b 2 = 2 a 2 = a = max { a,b } . If a < b then we have a + b + | a- b | 2 = a + b- ( a- b ) 2 = 2 b 2 = b = max { a,b } . In either case our equality holds. (b) (min { a,b } =- max {- a,- b } = a + b-| a- b | 2 ): First, by part (a) we have- max {- a,- b } =-- a- b + | - a + b | 2 = a + b- | (- 1)( a- b ) | 2 = a + b- | a- b | 2 And so the right hand equality holds. To show that min { a,b } =- max {- a,- b } we may assume, without loss of generality, that a b . Since a b we have min { a,b } = a . Furthermore a b implies that- a - b hence max {- a,- b } =- a . So we have min { a,b } = a =- max {- a,- b } . 10 (a) The l.u.b. of { 1 n : n N } is 1 since 1 n 1 for all n N and 1 is in the set. The g.l.b. of { 1 n : n N } is 0. To see that the g.l.b. is 0 note that 1 /n > 0 for all n N and by LUB2 no number greater then 0 will be a lower bound for this set.LUB2 no number greater then 0 will be a lower bound for this set....
View Full Document

Page1 / 2

AnalysisHW2 125A - MAT 125a, HW2 Solutions 7 (a) (max { a,b...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online