3

I know that one should use

$f\colon A\to B$

instead of

$f: A\to B$

Now I am wondering how one should write the declaration of domain and codomain of a function (i.e. f: A --> B) together with the assignment rule of the function (by which I mean a |--> f(a), where f(a) is the rule). I found the following possibilities:

1.

The function $f\colon A\to B : a\mapsto f(a)$ satisfies ...

2.

The function $f\colon A\to B$, $a\mapsto f(a)$ satisfies ...

3.

The function $f\colon A\to B, a\mapsto f(a)$ satisfies ...

4.

Using words:

The function $f\colon A\to B$ which is given by $a\mapsto f(a)$ satisfies ...

Do you know other possibilities? Which possibility do you recommend using?

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Nas is Like
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    Welcome to TeX.SE. Your posting appears to be eliciting subjective views. Separately, have you seen the posting Writing a nice function? – Mico Aug 07 '16 at 12:09
  • @Mico: Mhm, the post you linked to seems to focus more on how to write tex-code which generates the definition of a function where the assignment rule is under the declaration of domain and codomain. – Nas is Like Aug 07 '16 at 12:17
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    I'd use method 2. – egreg Aug 07 '16 at 12:56
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    I, too, see this more as a question on good writing style rather than on proper TeX usage. Though I am inclined to consider possibilities 1 and 3 as wrong, while the choice between 2 and 4 is more one of style. (Personally, I'd go for 4, but deleting “which is”.) To elaborate, I consider 1 and 3 as wrong because they smash to formulas into one. – Harald Hanche-Olsen Aug 07 '16 at 12:57
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    @Harald Hanche-Olsen: I think the same, maybe using ‘defined by’ and adding a comma before ‘satisfies’. – Bernard Aug 07 '16 at 13:01
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    I'm voting to close because this is a question about mathematical notation. – Henri Menke Aug 07 '16 at 13:22
  • Following the lead of lambda calculus it would by correct to write $f=(a\mapsto f(a) )$ or even 'anonymously' $(a\mapsto f(a) ) \colon A \to b$. – Michael Aug 24 '18 at 11:10

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