I was curious whether the definition that we had been taught in middle/high school of a "linear function" (a polynomial of degree at most one) was either wrong or a pedagogical simplification (operations on the natural numbers, the natural numbers themselves being a field, etc), and it seems like linear function does indeed have both definitions accepted. It is interesting though that the definition taught in grade school is not actually a generalization or specific case of a linear map but rather something related in terminology while, for example, other simplifications taught, like the natural numbers, tend to be specific cases of a general concept, like fields.