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The symmetric function equation of the Riemann zeta function in mathematics, also known as the Riemann Xi function; A universal set in set theory; A number used in the remainder term of Taylor's theorem that falls between the limits a and b
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
the set of natural numbers in set theory (although or N is more common in other areas of mathematics) an asymptotic dominant notation related to big O notation; in probability theory, a possible outcome of an experiment; the arithmetic function counting a number's distinct prime factors
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor [ 1 ] and are named after the symbol he used to denote them, the Hebrew letter aleph (ℵ).
The boundary of a set in topology. The boundary operator on a chain complex in homological algebra. The boundary operator of a differential graded algebra. The conjugate of the Dolbeault operator on complex differential forms. The boundary ∂(S) of a set of vertices S in a graph is the set of edges leaving S, which defines a cut.
2. Without a subscript, denotes the absolute complement; that is, =, where U is a set implicitly defined by the context, which contains all sets under consideration. This set U is sometimes called the universe of discourse. × (multiplication sign) See also × in § Arithmetic operators.
In certain contexts, zero and nothing are interchangeable, as is "null". However, in mathematics and many scientific disciplines, a distinction is made (see null). The number 0 is represented by zero while null is a representation of an empty set {}.
A bijective function, f: X → Y, from set X to set Y demonstrates that the sets have the same cardinality, in this case equal to the cardinal number 4. Aleph-null, the smallest infinite cardinal. In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set.