Well, i was reading a book lately about functions, and when it came to define the equality of two functions it defined something like this:(adsbygoogle = window.adsbygoogle || []).push({});

Let f:A->B and g:C->D be two functions.

We say that these two functions are equal if:

1.A=C

2.B=D and

3.f(x)=g(x) for all x in A=C.

I guess i have always overlooked it, but is 2. a little bit redundant. I mean, would a more precise statement be to say that if: ran{f}=ran{g}, rather than in terms of Codomains of these functions?

The reason i say this is that, for example:

Let: f:N-->R be a function from Naturals to Reals defined as follows: f(n)=n+1

and, let g:N-->Z be a function from Naturals to integers defined also as: g(n)=n+1

From here we see that their domains are the same, the ranges are the same and also f(n)=g(n) for every n in the domain. Can we say from here that these two functions are the same, or not? I would say yes, but maybe i am overlooking something.

THnx

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# Quick questions about equality of functions!

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