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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
If E is a logical predicate, means that there exists at least one value of x for which E is true. 2. Often used in plain text as an abbreviation of "there exists". ∃! Denotes uniqueness quantification, that is, ! means "there exists exactly one x such that P (is true)".
E notation, or scientific notation, a way of writing very large and very small numbers such as 5E7; ∃ (a backwards E; U+2203) or existential quantification, the symbol for "there exists...", in predicate logic; ∃!, meaning "there exists only one" (or "there exists exactly one"), see Uniqueness quantification
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 logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
There exists an x such that ... For at least one x, .... Keywords for uniqueness quantification include: For exactly one natural number x, ... There is one and only one x such that .... Further, x may be replaced by a pronoun. For example, For every natural number, its product with 2 equals to its sum with itself. Some natural number is prime.
Existence monism posits that, strictly speaking, there exists only a single thing, the universe, which can only be artificially and arbitrarily divided into many things. [ 2 ] Substance monism asserts that a variety of existing things can be explained in terms of a single reality or substance. [ 3 ]