As the title says, what does the notation $-S$ mean if $S$ is a set? For instance, in the context of something like $S \cup -S = F$, where $F$ is a field and $S$ is a subset of $F$?

Thanks in advance.

  • 1
    $\begingroup$ In this precise situation, $-S=\{-s,\,s \in S\}$. $\endgroup$
    – Aphelli
    Commented Jul 25, 2019 at 7:17
  • $\begingroup$ Straight-forward answer. Thank you. $\endgroup$
    – Tim
    Commented Jul 25, 2019 at 7:18

1 Answer 1


A possible interpretation in sets is $-S=\{x\in F : x \not \in S\}$ and this satisfies $S \cup -S = F$

But you say $F$ is field. So another possible interpretation is $-S=\{x\in F : -x \in S\}$, which need not satisfy $S \cup -S = F$

Given this ambiguity, it should be clear that a definition needs to be given by the user


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