ConceptCauchy sequence
Cauchy Sequence
A sequence whose terms become arbitrarily close to one another as the index increases; that is, for every positive number ε there exists an N such that whenever m and n are greater than N, the distance between the terms of the sequence is less than ε.
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Oct 27
The validity of the Bolzano-Weierstrass theorem depends on the completeness of the real numbers (the least upper bound property), and completeness is precisely the core property that the Cauchy sequence construction of the real numbers is meant to guarantee.
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