Thread: Functions; How do they work?

I was just wondering why functions can only have one output per input?

Because functions are defined that way. All functions are mappings. There are mappings that are not functions.

Originally Posted by Nervous

I was just wondering why functions can only have one output per input?

That is a requirement in the definition of function.
A relation on a set can have more than one output per input.
A function is a particular type of relation, no two pairs can have the same first term.

Originally Posted by MathoMan

There are mappings that are not functions.

Where did you get that? See this page.

Maybe a relation is a better term - English is not my native language so unfortunately things get lost in translation.

Originally Posted by Plato

Where did you get that? See this page.

My mistake. Explained in a post above.

Well, that Wikipedia entry not withstanding, I feel that "mapping" is a much vaguer term than "function".