I understand that the domain of a function is the set of all input values, but in some textbooks, the domain is an element of that set of input values. How can a set also be a subset of that set?. This is what I'm confused about.


1 Answer 1


Not sure, but maybe this answers your question.

In ordinary set-theory it does not happen that a set (e.g. the domain of a function) is an element of itself.

What I did encounter for a function $f:X\to Y$ is the notation $f(X)$.

This however does not mean that $X$ must be looked in that context at as an input value for the function $f$, but is only a notation for the set: $$\{f(x)\mid x\in X\}\subseteq Y$$

This notation is used not only for $X$ itself but also subsets $A\subseteq X$:$$f(A):=\{f(x)\mid x\in A\}\subseteq Y$$

  • $\begingroup$ Maybe also mention it generalises to arbitrary subsets of X $\endgroup$
    – user359302
    Feb 17, 2019 at 13:00
  • $\begingroup$ @alkchf I followed your advice. $\endgroup$
    – drhab
    Feb 17, 2019 at 13:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.