I'm not quite sure why this seems to be so controversial, except for the light abuse of notation in my english. Saying that f: X->Y means f maps an input from domain X to output in range Y is to say that we are defining a function -- and labeling it f, since it could just as easily be labeled g and still be the same function. Defining is naming -- naming is labeling [with scope].
It's not defining a function though, it's describing (by one aspect) a whole class of functions.
Take:
f: ints -> ints
f can be 'add1', 'identity', 'double', etc.
If you know that, and calling it 'defining a function' is just loose English (you didn't mean completely defining) then fine, but that's what's confusing people.
It read to me like you thought it was equivalent to a function definition in code, X & Y described what would actually happen over different inputs, so I was just trying to explain, didn't mean to offend if you knew already.
Oooh, I see what you're saying. For want of an "s". Yes, in this context, I am aware that it is a whole class of functions -- and that f is a label being affixed to that class of functions. Sorry for the confusion -- that makes much more sense now.
No offense received -- was just genuinely confused as to why it netted two comments and a few downvotes for a seemingly uncontroversial statement. But then again, we're talking mathematical logic here, so loose english is of course reasonably discouraged.
Thanks for the clarification, and I hope you have a great evening!
