# 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.

25 results; page 1/1.

## Question 16951: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0051`; number: 16951
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0051/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0051/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0051.json)

## Question 16952: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0052`; number: 16952
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0052/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0052/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0052.json)

## Question 16953: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0053`; number: 16953
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0053/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0053/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0053.json)

## Question 16954: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0054`; number: 16954
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0054/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0054/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0054.json)

## Question 16955: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0055`; number: 16955
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0055/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0055/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0055.json)

## Question 16956: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0056`; number: 16956
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0056/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0056/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0056.json)

## Question 16957: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0057`; number: 16957
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0057/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0057/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0057.json)

## Question 16958: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0058`; number: 16958
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0058/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0058/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0058.json)

## Question 16959: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0059`; number: 16959
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0059/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0059/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0059.json)

## Question 16960: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0060`; number: 16960
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0060/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0060/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0060.json)

## Question 16961: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0061`; number: 16961
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0061/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0061/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0061.json)

## Question 16962: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0062`; number: 16962
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0062/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0062/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0062.json)

## Question 16963: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0063`; number: 16963
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0063/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0063/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0063.json)

## Question 16964: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0064`; number: 16964
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0064/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0064/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0064.json)

## Question 16965: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0065`; number: 16965
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0065/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0065/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0065.json)

## Question 16966: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0066`; number: 16966
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0066/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0066/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0066.json)

## Question 16967: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0067`; number: 16967
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0067/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0067/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0067.json)

## Question 16968: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0068`; number: 16968
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0068/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0068/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0068.json)

## Question 16969: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0069`; number: 16969
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0069/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0069/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0069.json)

## Question 16970: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0070`; number: 16970
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0070/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0070/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0070.json)

## Question 16971: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0071`; number: 16971
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0071/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0071/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0071.json)

## Question 16972: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0072`; number: 16972
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0072/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0072/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0072.json)

## Question 16973: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0073`; number: 16973
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0073/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0073/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0073.json)

## Question 16974: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0074`; number: 16974
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0074/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0074/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0074.json)

## Question 16975: An Independent Family Gives Only a Lower Bound

- ID: `q-20261014-advance-20261102-r01-vector-space-dimension-0075`; number: 16975
- Processing: second_context_reviewed
- MKO: [mko-vector-space-dimension](/en/mko/mko-vector-space-dimension/)
- Family: [qf-mod33-dimension-independent-lower-bound](/en/explore/?family=qf-mod33-dimension-independent-lower-bound)
- Batch: [batch-20261014-advance-20261102-r01-vector-space-dimension-foundations](/en/explore/?batch=batch-20261014-advance-20261102-r01-vector-space-dimension-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0075/) / [Markdown](/en/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0075/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261102-r01-vector-space-dimension-0075.json)