Search results
Results from the WOW.Com Content Network
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.
It might be a statement which begins with the phrase "there exist(s)", or it might be a universal statement whose last quantifier is existential (e.g., "for all x, y, ... there exist(s) ..."). In the formal terms of symbolic logic , an existence theorem is a theorem with a prenex normal form involving the existential quantifier , even though in ...
which completes the proof that 3 is the unique solution of + =. In general, both existence (there exists at least one object) and uniqueness (there exists at most one object) must be proven, in order to conclude that there exists exactly one object satisfying a said condition.
The aleph numbers differ from the infinity commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...
The absolute infinite (symbol: Ω), in context often called "absolute", is an extension of the idea of infinity proposed by mathematician Georg Cantor.It can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite.
Nevertheless, infinite sets of different cardinalities exist, as Cantor's diagonal argument shows. Cantor's diagonal argument (among various similar names [ note 1 ] ) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are ...
Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many. "For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always ...