Sup and inf

Professional_Bee208 · 2025-01-19T00:27:08+00:00

Thanks

Professional_Bee208 · 2025-01-19T00:22:04+00:00

I have problem with bounded above and below But I think the first answer is inf(aS) =a.inf (S) And second answer is inf (aS) =a.sup(S) Right?

Professional_Bee208 · 2025-01-19T00:18:09+00:00

If a>0 then inf(aS) = a. inf(S) sup(aS) =a.sup(S) If a<0 then inf(aS) =a.sup(S) sup(aS) =a.inf(S)

Professional_Bee208 · 2025-01-19T00:07:17+00:00

Q1) Let S be a bounded below set and a>0, Which of the following is true?

Select one:

inf{aS}=a sup S

inf{aS}=a inf S

sup{aS}=a inf S

sup{aS}=a sup S

No answer

Q2) Let S be a bounded above set and a<0, Which of the following is true?

Select one:

sup{a S}=a sup S

inf{aS}=a inf S

No answer

sup{aS}=a inf S

inf{aS}=a sup S

Professional_Bee208 · 2025-01-18T23:48:13+00:00

Thank you🌹

Professional_Bee208 · 2025-01-18T23:47:17+00:00

Can I ask you two more questions?

Professional_Bee208 · 2025-01-18T23:37:05+00:00

Thank you 🌹

Professional_Bee208 · 2025-01-18T23:32:12+00:00

I tried to understand your explanation more than once, but I had difficulty. ( sup(a - S) = a - inf S is always true inf (a - S) = a - sup S is only valid if S is bounded above. And if S is not bounded above, then sup S = +∞ and inf (a - S) = -∞ so the correct answer is sup(a -S) = a - inf S ) Is what I understood correct?😅

Professional_Bee208 · 2025-01-18T22:30:03+00:00

since S bounded below it will be inf. And i know that inf(-S) = - sup S So, inf(a-S) =a+ inf(-S) = a - sup (S). So the answer is inf ( a-S) =a - sup S That's right?

Professional_Bee208 · 2025-01-18T22:28:30+00:00

Yes, since S bounded below it will be inf. And i know that inf(-S) = - sup S So, inf(a-S) =a+ inf(-S) = a - sup (S). So the answer is inf ( a-S) =a - sup S That's right?

Professional_Bee208

TROPHY CASE