| I'll try one last time. > I think you are not a mathematician Guess again. > Example: Jellyfish is not a jelly and not a fish. Biologists have got it all wrong! You have a problem with reading comprehension. I never said any mathematician was wrong. Think about namespaces for a moment, like in programming. There are two namespaces here: The analysis namespace and the foundations namespace. In either of those two namespaces, the word "mapping" means what you're describing: an arbitrary subset F of A×B for which every element of a ∈ A occurs as the first component in a unique element (x,y) ∈ F. But the term "function" has a different meaning in each of the two namespaces. The word "function" in the analysis namespace defines it to ONLY EVER be a mapping S -> R or S -> C, where S is a subset of C^n or R^n. The word "function" is not allowed to be used - within this namespace - to denote anything else. The word "function" in the foundations namespace defines it to be any mapping whatsoever. Hopefully, now you'll get it. |