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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
Substance monism posits that only one kind of substance exists, although many things may be made up of this substance, e.g., matter or mind. Dual-aspect monism is the view that the mental and the physical are two aspects of, or perspectives on, the same substance.
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)".
if and only if, iff, xnor propositional logic, Boolean algebra: is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.
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 ...
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.
One logo depicts a small heart surrounded by a larger heart, symbolizing a relationship between an pedophile and minor girl. Another logo resembles a butterfly and represents non-preferential ...
In the theory of partial orders with one relation symbol ≤, one could define s = t to be an abbreviation for s ≤ t t ≤ s. In set theory with one relation ∈, one may define s = t to be an abbreviation for ∀x (s ∈ x ↔ t ∈ x) ∀x (x ∈ s ↔ x ∈ t). This definition of equality then automatically satisfies the axioms for equality.