# 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 2/4. ## Question 11126: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0076`; number: 11126 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0076/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0076/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0076.json) ## Question 11127: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0077`; number: 11127 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0077/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0077/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0077.json) ## Question 11128: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0078`; number: 11128 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0078/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0078/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0078.json) ## Question 11129: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0079`; number: 11129 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0079/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0079/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0079.json) ## Question 11130: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0080`; number: 11130 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0080/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0080/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0080.json) ## Question 11131: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0081`; number: 11131 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0081/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0081/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0081.json) ## Question 11132: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0082`; number: 11132 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0082/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0082/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0082.json) ## Question 11133: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0083`; number: 11133 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0083/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0083/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0083.json) ## Question 11134: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0084`; number: 11134 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0084/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0084/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0084.json) ## Question 11135: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0085`; number: 11135 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0085/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0085/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0085.json) ## Question 11136: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0086`; number: 11136 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0086/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0086/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0086.json) ## Question 11137: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0087`; number: 11137 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0087/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0087/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0087.json) ## Question 11138: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0088`; number: 11138 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0088/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0088/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0088.json) ## Question 11139: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0089`; number: 11139 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0089/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0089/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0089.json) ## Question 11140: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0090`; number: 11140 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0090/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0090/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0090.json) ## Question 11141: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0091`; number: 11141 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0091/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0091/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0091.json) ## Question 11142: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0092`; number: 11142 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0092/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0092/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0092.json) ## Question 11143: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0093`; number: 11143 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0093/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0093/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0093.json) ## Question 11144: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0094`; number: 11144 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0094/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0094/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0094.json) ## Question 11145: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0095`; number: 11145 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0095/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0095/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0095.json) ## Question 11146: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0096`; number: 11146 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0096/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0096/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0096.json) ## Question 11147: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0097`; number: 11147 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0097/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0097/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0097.json) ## Question 11148: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0098`; number: 11148 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0098/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0098/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0098.json) ## Question 11149: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0099`; number: 11149 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0099/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0099/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0099.json) ## Question 11150: A Missing Midpoint Refutes Convexity, but a Present One Does Not Prove It - ID: `q-20261013-advance-20261024-r07-convex-set-0100`; number: 11150 - Processing: second_context_reviewed - MKO: [mko-convex-set](/en/mko/mko-convex-set/) - Family: [qf-mod24-convexset-finite-midpoint-counterexample](/en/explore/?family=qf-mod24-convexset-finite-midpoint-counterexample) - Batch: [batch-20261013-advance-20261024-r07-convex-set-foundations](/en/explore/?batch=batch-20261013-advance-20261024-r07-convex-set-foundations) - [Derivation](/en/questions/q-20261013-advance-20261024-r07-convex-set-0100/) / [Markdown](/en/questions/q-20261013-advance-20261024-r07-convex-set-0100/index.md) / [JSON](/data/question-derivations/questions/q-20261013-advance-20261024-r07-convex-set-0100.json) [Next](/en/explore/index.md?mko=mko-convex-set&page=3)