Complete (English)
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Definition (undergraduate level)
Of a metric space: having the property that every Cauchy sequence is convergent.
Of a normed vector space: having the property that the corresponding metric space (with the natural metric) is complete in the sense above. Such a space is called a Banach space.
A logical system is complete if everything that can be stated within the system can be either proved or disproved within the system.
Of a normed vector space: having the property that the corresponding metric space (with the natural metric) is complete in the sense above. Such a space is called a Banach space.
A logical system is complete if everything that can be stated within the system can be either proved or disproved within the system.
Relations
- broader:
- (en) Property
- references:
- (en) Banach space
- (en) Cauchy sequence
- (en) Metric space
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