I am currently watching (on YouTube) Fredric Schuller's lectures given in 2015 at The WE-Heraeus International Winter School on Gravity and Light and have a question about how Dr. Schuller talks about maps.
He starts by stating the following:
Let $M, N $ be sets and a map $f: M \to N$ where $m \in M$ such that $f: m \mapsto f(m) $.
He then goes on to elaborate and says "if $M, N \subset \mathbb{R}$ then we can give a definite prescription $f(m)=m^2$." What does he mean by a definite prescription? I have provided the link at the bottem of this post to the lecture if anyone would like to take a listen.
Lecture 1: Topology (International Winter School on Gravity and Light 2015)