an infinite sequence,
x _{1} ,
x _{2} , …, whose terms are points in
E_{k}, in
which there exists a point
y such that the limit as
n goes to infinity of
x_{n} =
y if and only if for every ε>0, there exists a number
N such that
i >
N and
j >
N implies |
x_{i} −
x_{j} |< ε.
Also called Cauchy sequence, convergent sequence. Compare
complete ( def 10b ).