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Cauchy Sequence of Real Numbers

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def:cauchy-sequence-real-c54-2026a
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Statement

A sequence (an)n=1∞(a_n)_{n=1}^\infty of real numbers is called a Cauchy sequence if for every ε>0\varepsilon>0 there exists N∈NN\in\mathbb{N} such that for all integers m,n≥Nm,n\ge N,

∣an−am∣<ε.|a_n-a_m|<\varepsilon.

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