Is there some compact notation for saying "all the elements of a set"?

Just trying to save time and be concise really when:

$\forall x\in S:P(x)$ is a bit long-winded to some potential alternative:

$P(\bar S)$

  • 2
    $\begingroup$ I feel that $\forall x \in S \, : P(x)$ is the commonly accepted notation. One could use something like $P|_S \equiv \operatorname{true}$, but this looks slightly weird. $\endgroup$ – lisyarus Jun 15 '18 at 15:25
  • 1
    $\begingroup$ If you're not doing something closely related to logic, it's more common to be even more "long-winded" and to use words, rather than the symbol $\forall$. $\endgroup$ – Mark S. Jun 16 '18 at 20:12

Sometimes people define $P(S)$ to mean $\forall x\in S, P(x)$. If you explicitly define it this way, then you can use it this way.


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.