# Pointwise combination of functions

From Calculus

## Definition

### For a binary operation

Suppose we have a binary operation (such as addition, subtraction, multiplication, division) on real numbers. A **pointwise combination** of two functions that take real values is a new function that first applies the two functions individually and then applies the binary operation.

For instance, pointwise sum of functions and is the function . Similarly, pointwise product of functions and is thee function .

The term **pointwise** is an allusion to the inputs to the function as points (thinking of the function geometrically). *Pointwise* refers to the idea that *for each point, the values of the functions at that point are combined.*