Cauchy sequence

Uncommon card · No. 165192

In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from each other. Cauchy sequences are named after Augustin-Louis Cauchy; they may occasionally be known as fundamental sequences. It is not sufficient for each term to become arbitrarily close to the preceding term. For instance, in the sequence of square roots of natural numbers: a n = n , {\displaystyle a_{n}={\sqrt {n}},} the consecutive terms become arbitrarily close to each other – their differences a n + 1 − a...

Read on Wikipedia · Image Krishnavedala, CC0