When showing a sequence is cauchy, we are trying show validity of an inequality whose RHS is epsilon. I noticed that authors try to avoid making RHS epsilon multiplied by a constant apart from 1. For example, when showing sum of two cauchy sequences is also cauchy, they set their epsilons as epsilon/2 at the beginning and when you add them you have epsilon. But why do we bother? What is wrong with obtaining 2epsilon at RHS?
2026-04-07 14:35:36.1775572536
about cauchy sequences' epsilons
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