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I am reading a logic book (section 17.5) and there is some terminology in it about functions. It says that

We also say a function f is

  • from a set A if its domain is a subset of A

  • on a set A if its domain is A

  • into a set B if its range is a subset of B

  • onto a set B if its range is B

I agree about the last two definition about codomain, but the first two confused me, because I have known that :

a function from a set X to a set Y assigns to each element of X exactly one element of Y

(https://en.wikipedia.org/wiki/Function_(mathematics))

I have never heard "on a set A if its domain is A", can you please say which terminology is correct, wiki or the book ? Many book use "from a set ..." wording and i understand all elements in the given set as domain, not its some subsets.

disclaimer: there is some suggestion links about my question such that they may be similar,but i have confused about the domain terminology bot codomain part

  • If it says on a set A, doesn't that just mean that it is a part of set A, hence a subset of A? – ThankYouForFlyingRyanair Feb 07 '25 at 11:56
  • @MauroALLEGRANZA i could not understand what you mean –  Feb 07 '25 at 12:11
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    That's a confusing terminology. A function pretty much always is defined on full domain. What the book refers to is also known as partial function, but in a confusing way. – freakish Feb 07 '25 at 12:59
  • @MauroALLEGRANZA the question in your link is about the codomain part, but i agree with the book and wiki about the codomain part,i.e, into a set and onto a set. my confusion is about the domain definition –  Feb 07 '25 at 14:56
  • @freakish i always see and read what you commented but when i see the distinction between "from" and "on" while talking about the domain, i thought that i may miss somethings –  Feb 07 '25 at 14:59

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