if S is non empty and it has a lower bound, then it has an...

50.1K

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Question

Advance Math

if S is non empty and it has a lower bound, then it has an infimum, inf S
Start of proof:
b<=s for all s in S
LB: {y in R:y<=S, for all s in S}
LB is bounded above by X and LB is non empty since b is in LB
Find supLB=infS, thats what needs to be completed

Answer & Explanation Solved by verified expert

3.6 Ratings (356 Votes)

As you have not clearly mentioned the nature of S so I amanswering for two different cases with two different results1 S is a set of rational NumbersLets define S asHere S is non empty as 49 etc belong to SAlso it is See Answer

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if S is non empty and it has a lower bound, then it has an...

50.1K

Verified Solution

Question

Advance Math

if S is non empty and it has a lower bound, then it has an infimum, inf S
Start of proof:
b<=s for all s in S
LB: {y in R:y<=S, for all s in S}
LB is bounded above by X and LB is non empty since b is in LB
Find supLB=infS, thats what needs to be completed

Answer & Explanation Solved by verified expert

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if S is non empty and it has a lower bound, then it has an...

50.1K

Verified Solution

Question

Advance Math

if S is non empty and it has a lower bound, then it has an infimum, inf SStart of proof:b<=s for all s in SLB: {y in R:y<=S, for all s in S}LB is bounded above by X and LB is non empty since b is in LBFind supLB=infS, thats what needs to be completed

Answer & Explanation Solved by verified expert

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Other questions asked by students

if S is non empty and it has a lower bound, then it has an infimum, inf S
Start of proof:
b<=s for all s in S
LB: {y in R:y<=S, for all s in S}
LB is bounded above by X and LB is non empty since b is in LB
Find supLB=infS, thats what needs to be completed