pointwise

In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function 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.

== Pointwise operations == thumb|Pointwise sum (upper plot, violet) and product (green) of the functions sine function|sin (lower plot, blue) and ln (red). The highlighted vertical slice shows the computation at the point x=2π. ===Formal definition=== A binary operation on a set can be lifted pointwise to an operation on the set of all functions from to as follows: Given two functions and , define the function by