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pronunciation clarified
{{Math-m}}
{{Math-m}}
:''The reader should be familiar with the material in the [[Limit (mathematics)]] page.''
:''The reader should be familiar with the material in the [[Limit (mathematics)]] page.''
A '''Cauchy sequence''' (pronounced KOH-she) is an infinite sequence that converges in a particular way. This type of convergence has a far-reaching significance in mathematics. Cauchy sequences are named after the French mathematician Augustin Cauchy (1789-1857).
A '''Cauchy sequence''' (pronounced CO-she) is an infinite sequence that converges in a particular way. This type of convergence has a far-reaching significance in mathematics. Cauchy sequences are named after the French mathematician Augustin Cauchy (1789-1857).
There is an extremely profound aspect of convergent sequences. '''A sequence of numbers in some set might converge to a number not in that set.''' The famous example of this is that a sequence of [[rational number|rationals]] might converge, but not to a rational number. For example, the sequence
There is an extremely profound aspect of convergent sequences. '''A sequence of numbers in some set might converge to a number not in that set.''' The famous example of this is that a sequence of [[rational number|rationals]] might converge, but not to a rational number. For example, the sequence