Ads
related to: math ordinaleducation.com has been visited by 100K+ users in the past month
- Education.com Blog
See what's new on Education.com,
explore classroom ideas, & more.
- Guided Lessons
Learn new concepts step-by-step
with colorful guided lessons.
- Lesson Plans
Engage your students with our
detailed lesson plans for K-8.
- Interactive Stories
Enchant young learners with
animated, educational stories.
- Education.com Blog
Search results
Results from the WOW.Com Content Network
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, ... Encyclopedia of Mathematics, EMS Press, 2001 [1994]
Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of year; Regnal ordinal – Ordinal numbers used to distinguish among persons with the same name who held the same office
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion .
Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets. Infinitesimals: These are smaller than any positive real number, but are nonetheless greater than zero.
The standard definition of ordinal exponentiation with base α is: =, =, when has an immediate predecessor . = {< <}, whenever is a limit ordinal. From this definition, it follows that for any fixed ordinal α > 1, the mapping is a normal function, so it has arbitrarily large fixed points by the fixed-point lemma for normal functions.
The cardinality of any infinite ordinal number is an aleph number. Every aleph is the cardinality of some ordinal. The least of these is its initial ordinal. Any set whose cardinality is an aleph is equinumerous with an ordinal and is thus well-orderable. Each finite set is well-orderable, but does not have an aleph as its cardinality.
In mathematics, the first uncountable ordinal, traditionally denoted by or sometimes by , is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum (least upper bound) of all countable ordinals.
Buchholz (1986) described the following system of ordinal notation as a simplification of Feferman's theta functions. Define: Ω ξ = ω ξ if ξ > 0, Ω 0 = 1; The functions ψ v (α) for α an ordinal, v an ordinal at most ω, are defined by induction on α as follows: ψ v (α) is the smallest ordinal not in C v (α)
Ads
related to: math ordinaleducation.com has been visited by 100K+ users in the past month