# OCME · 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 4/4.

## Question 15876: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0001`; number: 15876
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0001/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0001/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0001.json)

## Question 15877: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0002`; number: 15877
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0002/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0002/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0002.json)

## Question 15878: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0003`; number: 15878
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0003/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0003/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0003.json)

## Question 15879: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0004`; number: 15879
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0004/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0004/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0004.json)

## Question 15880: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0005`; number: 15880
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0005/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0005/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0005.json)

## Question 15881: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0006`; number: 15881
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0006/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0006/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0006.json)

## Question 15882: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0007`; number: 15882
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0007/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0007/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0007.json)

## Question 15883: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0008`; number: 15883
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0008/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0008/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0008.json)

## Question 15884: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0009`; number: 15884
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0009/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0009/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0009.json)

## Question 15885: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0010`; number: 15885
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0010/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0010/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0010.json)

## Question 15886: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0011`; number: 15886
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0011/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0011/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0011.json)

## Question 15887: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0012`; number: 15887
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0012/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0012/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0012.json)

## Question 15888: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0013`; number: 15888
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0013/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0013/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0013.json)

## Question 15889: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0014`; number: 15889
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0014/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0014/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0014.json)

## Question 15890: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0015`; number: 15890
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0015/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0015/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0015.json)

## Question 15891: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0016`; number: 15891
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0016/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0016/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0016.json)

## Question 15892: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0017`; number: 15892
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0017/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0017/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0017.json)

## Question 15893: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0018`; number: 15893
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0018/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0018/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0018.json)

## Question 15894: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0019`; number: 15894
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0019/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0019/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0019.json)

## Question 15895: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0020`; number: 15895
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0020/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0020/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0020.json)

## Question 15896: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0021`; number: 15896
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0021/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0021/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0021.json)

## Question 15897: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0022`; number: 15897
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0022/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0022/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0022.json)

## Question 15898: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0023`; number: 15898
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0023/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0023/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0023.json)

## Question 15899: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0024`; number: 15899
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0024/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0024/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0024.json)

## Question 15900: A Complete Finite List Gives an At-Most-Countable Certificate

- ID: `q-20261014-advance-20261031-r01-at-most-countable-set-0025`; number: 15900
- Processing: second_context_reviewed
- MKO: [mko-at-most-countable-set](/en/mko/mko-at-most-countable-set/)
- Family: [qf-mod31-countable-finite-certificate](/en/explore/?family=qf-mod31-countable-finite-certificate)
- Batch: [batch-20261014-advance-20261031-r01-at-most-countable-set-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r01-at-most-countable-set-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0025/) / [Markdown](/en/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0025/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r01-at-most-countable-set-0025.json)