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When no confusion is possible, notation f(S) is commonly used. 1. Closed interval : if a and b are real numbers such that a ≤ b {\displaystyle a\leq b} , then [ a , b ] {\displaystyle [a,b]} denotes the closed interval defined by them.
Mar 10, 2021 · Perhaps to avoid this confusion, some systems use a different symbol for conjunction. For example, ‘∧’ is a counterpart to the symbol used for disjunction. Sometimes a single dot, ‘•’, is used. In some older texts, there is no symbol for conjunction at all; ‘ A A and B B ’ is simply written ‘ AB A B.’.
Let us use *c2' to abbreviate the phrase 'Church's favorite proposition', and adopt the convention of surrounding a sen-tence with '[ ]2 in order to obtain a designation of the sense of (i.e., the propo-sition expressed by) the sentence. According to the Frege-Church theory of meaning, a proposition is true if it is a concept of, well, The True.
- C. Anthony Anderson
- 1987
As a rule of thumb I use type-writer font for quantifier expressions and italics for the signified quantifiers. In logical languages, on the other hand, it is convenient to abuse notation somewhat by using the same symbol for both the expression and the quantifier, when no confusion results.
Sense is a fact about the language, denotation is a fact about the world or situation under discussion. Two expressions that have different senses may still have the same denotation in a particular situation.
Jan 13, 2015 · Short answer based on my opinions: (1) people don't learn grammar, (2) notation (e.g. lambda abstraction) for expressing things both precisely and conveniently is unfamiliar, and (3) people don't properly learn about dependent variables, and are instead trained to interpret everything as functions. – user14972.
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Aug 19, 2004 · This is notation that is used to abbreviate universally quantified variables. In modern notation, these become ∀ x (φ x ⊃ ψ x) and ∀ x (φ x ≡ ψ x), respectively. See the definitions for this notation at the end of Section 3.2 below. ! pronounced “shriek”; indicates that a function is predicative, as in φ!x or φ!xˆ.
