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Yes I can see that, one is 'f', the other is 'g', are you implying this is all that's needed? What do f or g do with the numbers? Maybe someone could say "the function is what maps the domain to its range", perhaps?

I still think you were only being precious about mathematical terminology. Studying calculus usually involves a bit of set theory. And studying electronics usually means you end up talking about functions being 'the same as' their output.

This is understood to be mere convenience, and is also understood to not be actually mathematically accurate, but it happens, I have been to lectures where this becomes the norm, say. What's the big deal with doing this, as I outlined in previous posts to this thread?

P.S. If a range (which can be continous) can be a domain, why is it wrong to say "a continuous domain", again?

P.P.S. Isn't it inaccurate to say:

The functions f: {(0,1), (1,1), (2, 2), (3, 3)} and g: {(0, 3), (1, 2), (2, 1), (3, 1)} have exactly the same Domain: {0, 1, 2, 3} and exactly the same range, {0, 1, 2, 3}, which are themselves identical

Both domains are indeed the same set of integers, and have identical ordering or collation, but the ranges have different ordering.

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Both domains are indeed the same set of integers, and have identical ordering or collation, but the ranges have different ordering.

Sorry, there was a typo in my example: g should be g: {(0, 3), (1, 2), (2, 1), (3, 0)}.

Now, the ranges are {0, 1, 2, 3} and {3, 2, 1, 0}, which are, of course the same set- order is not relevant in a set.

Yes I can see that, one is 'f', the other is 'g', are you implying this is all that's needed? What do f or g do with the numbers?

"All that's needed" for WHAT? The sets of ordered pairs show exactly what f and g "do with the numbers": f(0)= 3, f(1)= 1, f(2)= 2, f(3)= 3 (f is the "identity" function on its domain) while g(0)= 3, g(1)= 2, g(2)= 1, and g(3)= 0 (after my correction). If you do not understand in what sense these sets of ordered pairs ARE functions, then you seem to have trouble understanding the basic definition of "function" (and at least a little difficulty believing what I am saying). Please take the example I gave you and to your calculus lecturer, who, I am sure, is quite good, and ask him/her to explain the example to you.

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