8.1. Pointwise Convergence

Definition 8.1.5: Pointwise Convergence

A sequence of functions { fn(x) } with domain D converges pointwise if for each fixed x0 D in the domain the numeric sequence { fn(x0) } converges. In other words: for each fixed x0 and any given > 0 there exists a positive integer N such that
| fn(x0) - L | < whenever n N
for some limit L. Note that the limit L depends on x0, while the integer N depends on x0 and .

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