I found this symbol in a book I'm reading. Does anyone know what this symbol means? Does it mean for all js?

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1 Answer 1


It's universal quantifier that interpreted as "given any" or "for all". you can check definition of quantifiers.

  • $\begingroup$ Correct, but I'll add that the phrase is $\forall{j{\neq}i}$, not just $\forall{j}$ $\endgroup$ Commented Aug 26, 2021 at 1:12
  • $\begingroup$ @ZacharyVance Actually $\forall j\neq i$ is an abbreviation, which is not fully formalized, but usually does not raise interpretation issues. The proper form is $\forall j \in S : P(j)$ where $S$ is the set of all values that can be taken by the quantified variable $j$, and the predicate $P$ must be verified for each value. $\endgroup$
    – babou
    Commented Aug 26, 2021 at 12:53
  • $\begingroup$ I'm commenting on the highlighted phrase, not your answer. Think like a beginner. The highlighted phrase is not quite how you should read it: In english, "For all j, not equal to i P(x)" doesn't read correctly. Instead, highlight the phrase I list: in english "For all j not equal to i, P(x)" makes sense. $\endgroup$ Commented Aug 27, 2021 at 22:22

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