In calculus the definition of the limit L of a sequence of real numbers r1, r2,r3, … can b...

In calculus the definition of the limit L of a sequence of real numbers r1, r2,r3, … can be given as

if (and only if) for every  ϵ > 0 there exists a positive integer k so that for all integers n, if n > k then |rn – L|<ϵ.

In symbolic form this can be expressed as