APOLOGY: This question is asked by someone foreign to math, with the expectation that math.stackexchange can be a resource to (among other things) understand math concepts.
I'm a self-taught project-of programmer. I would like to understand "projection", beacuse it's used in functional programming (related to lamda calculus I hear), and in a database called MongoDB.
For the math term of projection Wikipedia links to "function composition", whose page in turn links to "pointwise".
The question is: What is “pointwise”, in the context of function composition?
So that (from wikipedia's "projection")
"In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent)."
Can be understood once (from wikipedia's "function composition"):
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
Thanks in advance.
Also, resources to material that can help with this kind of doubts are very much welcome