# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 100 results; page 1/4. ## Question 20501: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0001`; number: 20501 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0001/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0001/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0001.json) ## Question 20502: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0002`; number: 20502 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0002/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0002/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0002.json) ## Question 20503: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0003`; number: 20503 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0003/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0003/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0003.json) ## Question 20504: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0004`; number: 20504 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0004/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0004/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0004.json) ## Question 20505: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0005`; number: 20505 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0005/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0005/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0005.json) ## Question 20506: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0006`; number: 20506 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0006/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0006/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0006.json) ## Question 20507: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0007`; number: 20507 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0007/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0007/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0007.json) ## Question 20508: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0008`; number: 20508 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0008/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0008/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0008.json) ## Question 20509: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0009`; number: 20509 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0009/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0009/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0009.json) ## Question 20510: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0010`; number: 20510 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0010/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0010/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0010.json) ## Question 20511: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0011`; number: 20511 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0011/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0011/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0011.json) ## Question 20512: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0012`; number: 20512 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0012/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0012/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0012.json) ## Question 20513: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0013`; number: 20513 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0013/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0013/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0013.json) ## Question 20514: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0014`; number: 20514 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0014/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0014/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0014.json) ## Question 20515: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0015`; number: 20515 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0015/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0015/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0015.json) ## Question 20516: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0016`; number: 20516 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0016/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0016/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0016.json) ## Question 20517: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0017`; number: 20517 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0017/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0017/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0017.json) ## Question 20518: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0018`; number: 20518 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0018/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0018/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0018.json) ## Question 20519: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0019`; number: 20519 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0019/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0019/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0019.json) ## Question 20520: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0020`; number: 20520 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0020/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0020/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0020.json) ## Question 20521: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0021`; number: 20521 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0021/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0021/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0021.json) ## Question 20522: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0022`; number: 20522 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0022/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0022/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0022.json) ## Question 20523: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0023`; number: 20523 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0023/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0023/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0023.json) ## Question 20524: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0024`; number: 20524 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0024/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0024/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0024.json) ## Question 20525: Finite Nonempty Real Sets Attain Both Their Bounds - ID: `q-20261014-advance-20261107-r02-supremum-and-infimum-0025`; number: 20525 - Processing: second_context_reviewed - MKO: [mko-supremum-and-infimum](/en/mko/mko-supremum-and-infimum/) - Family: [qf-mod38-supinf-finite-extrema](/en/explore/?family=qf-mod38-supinf-finite-extrema) - Batch: [batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations](/en/explore/?batch=batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations) - [Derivation](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0025/) / [Markdown](/en/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0025/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261107-r02-supremum-and-infimum-0025.json) [Next](/en/explore/index.md?mko=mko-supremum-and-infimum&page=2)