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{{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