thus the graph of a function lives in a space whose dimension is the sum of the dimensions of the domain and codomain of .
it is convenient to denote a point in the graph of a function as . with and . but this presupposes that the "active" variables are the first variables, which is a problem, since we usually cannot use the same active variables at all points of the mainfold.
the graph of a partial function is the relation
- partial functions and are equal, , if .