Function defined on/over/from A to B

Question

how should one read

in plain English?
In the following sentence, for example:
"let f be a function defined on/over/from/(other) A to/(other) B"?

edit:
This post has been tagged as a possible duplicate to this question.
However, I originally I posted this as a followup question on the page in question, and has subsequently been deleted by a moderator:
deleted by ***♦ 16 hours ago
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and someone commented:
Hi @Mogu ... even for related questions, you can (and should) post it as a new question.

The question in the other post regarded the prepositions to be used with respect to the domain of a function, whereas mine is also concerned with its codomain, and whether or not the act of mentioning the codomain in a sentence changes what prepositions should be used to relate to its domain as well.

Daniel R. Collins · Answer

Personally, I would not want to stick more words into the verbalized phrase than there are symbols in the writing. I would prefer to vocalize the given expression as:

"f from A to B"

This might be part of a sentence like, "We define the function f from A to B in the following way...", and so forth.

Mitch · Answer

"Let f be a function from A to B"

if there is nothing else. Variations are on the 'to': 'into'/'onto' for injective/surjective function s respectively (if that is something you want to say there).

If the function is A -> A, you can say more compactly:

"Let f be a function on A."

Function defined on/over/from A to B

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