Table of Contents
16 relations: Aleph number, Beth number, Cambridge University Press, Cardinal number, Empty set, Fixed-point lemma for normal functions, Image (mathematics), Infimum and supremum, Limit ordinal, Monotonic function, Order topology, Ordinal arithmetic, Ordinal number, Set theory, Successor ordinal, Veblen function.
Aleph number
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.
See Normal function and Aleph number
Beth number
In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written \beth_0, \beth_1, \beth_2, \beth_3, \dots, where \beth is the Hebrew letter beth.
See Normal function and Beth number
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
See Normal function and Cambridge University Press
Cardinal number
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set.
See Normal function and Cardinal number
Empty set
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
See Normal function and Empty set
Fixed-point lemma for normal functions
The fixed-point lemma for normal functions is a basic result in axiomatic set theory stating that any normal function has arbitrarily large fixed points (Levy 1979: p. 117). Normal function and fixed-point lemma for normal functions are ordinal numbers.
See Normal function and Fixed-point lemma for normal functions
Image (mathematics)
In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f".
See Normal function and Image (mathematics)
Infimum and supremum
In mathematics, the infimum (abbreviated inf;: infima) of a subset S of a partially ordered set P is the greatest element in P that is less than or equal to each element of S, if such an element exists.
See Normal function and Infimum and supremum
Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Normal function and limit ordinal are ordinal numbers.
See Normal function and Limit ordinal
Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
See Normal function and Monotonic function
Order topology
In mathematics, an order topology is a specific topology that can be defined on any totally ordered set. Normal function and order topology are ordinal numbers.
See Normal function and Order topology
Ordinal arithmetic
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Normal function and ordinal arithmetic are ordinal numbers and set theory.
See Normal function and Ordinal arithmetic
Ordinal number
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. Normal function and ordinal number are ordinal numbers.
See Normal function and Ordinal number
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.
See Normal function and Set theory
Successor ordinal
In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α. Normal function and successor ordinal are ordinal numbers.
See Normal function and Successor ordinal
Veblen function
In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in. Normal function and Veblen function are ordinal numbers.
See Normal function and Veblen function
References
Also known as Derivative (set theory).