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I'm reading about an algorithm (it's a path-finding algorithm based on A*), and it contains a mathematical symbol I'm unfamiliar with: ∀
Here is the context:
v(s) ≥ g(s) = mins'∈pred(s)(v(s') + c(s', s)) ∀s ≠ sstart
Can someone explain the meaning of ∀?
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The symbol ∀ means “for all” or “for any”. The symbol ∃ means “there exists”. Finally we abbreviate the phrases “such that” and “so that” by the symbol or simply “s.t.”. When mathematics is formally written (as in our text), the use of these symbols is often suppressed.
∀ This symbol means for all (or sometimes, for every). For example, “∀ squares D, D is a rectangle”. ∃ This symbol means there exists. For example, “∃ a horse”. This symbol means there does not exist.
The ∀ symbol may look like the familiar capital “A” written upside down, but in mathematics (specifically in predicate calculus), the ∀ is a logic symbol or universal quantifier. You can use it in place of “for all.” This means that ∀ is a shorthand character you'll use when writing proofs, equations, and sets.
The logical symbol ∀, has the same shape as a sans-serif capital turned A. It is used to represent universal quantification in predicate logic, where it is typically read as "for all".
That's the "forall" (for all) symbol, as seen in Wikipedia's table of mathematical symbols or the Unicode forall character (\u2200, ∀).
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