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In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" [2] or "∃ =1". For example, the formal statement
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
Hence for decades, the canonical notation in philosophy and mathematical logic was (x)P to express "all individuals in the domain of discourse have the property P," and "(∃x)P" for "there exists at least one individual in the domain of discourse having the property P." Peano, who was much better known than Peirce, in effect diffused the ...
The negation of the sentence "For every x, if x is a philosopher, then x is a scholar" is logically equivalent to the sentence "There exists x such that x is a philosopher and x is not a scholar". The existential quantifier "there exists" expresses the idea that the claim "x is a philosopher and x is not a scholar" holds for some choice of x.
From the other direction, there has been considerable clarification of what constructive mathematics is—without the emergence of a 'master theory'. For example, according to Errett Bishop's definitions, the continuity of a function such as sin(x) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a ...
In symbolic logic, the universal quantifier symbol (a turned "A" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...