算法中的陌生符号: something 是什么意思？

我正在读一个算法(它是一个基于 A * 的路径寻找算法) ，它包含一个我不熟悉的数学符号: something

背景是这样的:

V (s)≥ g (s) = minS’∈ pred (s)(v (s’) + c (s’，s)) s ≠ s开始

谁能解释一下 something 的意思？

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最佳答案

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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In math, ∀ means FOR ALL.

Unicode character (\u2200, ∀).

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Can be read, "For all s such that s does not equal s[start]"

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The upside-down A symbol is the universal quantifier from predicate logic. (Also see the more complete discussion of the first-order predicate calculus.) As others noted, it means that the stated assertions holds "for all instances" of the given variable (here, s). You'll soon run into its sibling, the backwards capital E, which is the existential quantifier, meaning "there exists at least one" of the given variable conforming to the related assertion.

If you're interested in logic, you might enjoy the book Logic and Databases: The Roots of Relational Theory by C.J. Date. There are several chapters covering these quantifiers and their logical implications. You don't have to be working with databases to benefit from this book's coverage of logic.

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yes, these are the well-known quantifiers used in math. Another example is ∃ which reads as "exists".

http://en.wikipedia.org/wiki/Quantification


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