Re: Why f:domain->codomain instead of f:domain->range?
- From: Robert Low <mtx014@xxxxxxxxxxxxxx>
- Date: Mon, 30 Jan 2006 15:36:47 +0000
kj wrote:
I never understood why the notation
f:X->Y
instead of
f:X->f(X)
In other words, I don't understand the utility of the notion of a codomain. Why not make the definition of "function" be so that every function is surjective? I'm sure there are very good reasons for this, but I don't see them.
The only explanation I can think of is that there are often times
when it is much easier to describe a function's codomain than than
its range. Is this it?
Isn't it enough?
What's the range of f:R -> R, f(x) = x^8 - 2x^7 + 3.1x^6 - 3x^5 - 4x^4 + 2x^3 - 27x + 3?
If that isn't hard enough, I'm sure that there's a polynomial function out there whose range can't be expressed nicely.
Or if you want something stranger, what about the function
f:R -> {0,1}
f(x)= 0 if Goldbach's conjecture is true, 1 if it's false?
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