In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value
f
(
x
)
{\displaystyle f(x)}
of some function
f
.
{\displaystyle f.}
An important class of pointwise concepts are the pointwise operations, that is, operations defined on functions by applying the operations to function values separately for each point in the domain of definition. Important relations can also be defined pointwise.
How do I know whether or not the series
$$ \sum_{n=1}^\infty sin(\frac{n\pi}{2})sin(nx)$$
converges pointwise for all real x or not?
By the way am I right in thinking that converging pointwise for all real x means whatever x i plug into the series it converges to some finite value?
I was...