word choice - "Function defined on/over the set A"


For the mathematically inclined fellows:


If f is a function whose domain is the set A, do you say that f is defined on A or over A? Do both prepositions apply here or is the use of one of them decidedly wrong?



Answer



Generally, for mere functions I think defined on A is more common. A quick Google Books search* revealed examples of "defined over A", but that it's more common for a vector space or some more complex algebraic structure defined over A.


Searching Google Books for on.


Searching Google Books for over.


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