Interactive Real Analysis
- part of 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
.
Context
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 | <for some limit L. Note that the limit L depends on x0, while the integer N depends on x0 andN
.
Context