Logical expressions

Open formula

An open formula is a formula that contains at least one free variable. An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like true or false. An open formula can be transformed into a closed formula by applying quantifiers or specifying of the domain of discourse of individuals for each free variable denoted x, y, z....or x1, x2, x3.... This transformation is called capture of the free variables to make them bound variables, bound to a domain of individual constants. For example, when reasoning about natural numbers, the formula "x+2 > y" is open, since it contains the free variables x and y. In contrast, the formula "∃y ∀x: x+2 > y" is closed, and has truth value true. An example of closed formula with truth value false involves the sequence of Fermat numbers studied by Fermat in connection to the primality. The attachment of the predicate letter P (is prime) to each number from the Fermat sequence gives a set of false closed formulae when the rank n of the Fermat number is greater than 4. Thus the closed formula ∀n P(Fn) is false. (Wikipedia).

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From playlist Calculus

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This video explains how to use the closed formulas of common sequences to determine closed formulas for related sequences. mathispower4u.com

From playlist Sequences (Discrete Math)

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This video explains how to use the closed formulas of common sequences to determine closed formulas for related sequences. mathispower4u.com

From playlist Sequences (Discrete Math)

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From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)

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From playlist Sequences (Discrete Math)

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From playlist Real Analysis

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From playlist Real Analysis

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From playlist Proofs

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From playlist Microsoft® Excel® 2010 Step by Step Videos

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From playlist Microsoft Excel

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From playlist Excel Hash 2021

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From playlist Logic in Philosophy and Mathematics

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From playlist Excel Array Formulas Beg - Advanced

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From playlist Excel Formulas

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From playlist Basic Equations

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Related pages

Fermat number | Higher-order logic | Quantifier (logic) | Domain of discourse | Truth value | Natural number | Universal quantification | First-order logic | Predicate (mathematical logic) | Existential quantification