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There is a page named "Cardinal exponentiation" on Wikipedia
= κν·μν. Exponentiation is non-decreasing in both arguments: (1 ≤ ν and κ ≤ μ) → (νκ ≤ νμ) and (κ ≤ μ) → (κν ≤ μν). 2|X| is the cardinality of the power...26 KB (3,808 words) - 01:08, 27 April 2024
In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Exponentiation is written as bn, where b is the...104 KB (13,629 words) - 19:45, 18 July 2024- Ordinal arithmetic (redirect from Ordinal exponentiation)ordinal exponentiation and cardinal exponentiation, the two operations are quite different and should not be confused. The cardinal exponentiation AB is...36 KB (4,944 words) - 13:10, 12 July 2024
- Gimel function (category Cardinal numbers)gimel function is used for studying the continuum function and the cardinal exponentiation function. The symbol ℷ {\displaystyle \gimel } is a serif form...4 KB (470 words) - 17:06, 28 May 2024
- Continuum hypothesis (category Cardinal numbers)infinite cardinals as well as finite cardinals. Although the generalized continuum hypothesis refers directly only to cardinal exponentiation with 2 as...31 KB (3,962 words) - 18:18, 2 July 2024
Cartesian product (section Cardinality)frequently denoted XI. This case is important in the study of cardinal exponentiation. An important special case is when the index set is N {\displaystyle...21 KB (2,821 words) - 15:28, 14 June 2024- Equinumerosity (category Cardinal numbers)B)C ~ AC × BC (AB)C ~ AB×C These properties are used to justify cardinal exponentiation. Furthermore, the power set of a given set A (the set of all subsets...14 KB (1,814 words) - 19:41, 27 April 2024
- Beth number (category Cardinal numbers){\displaystyle \{0,1\}} , the cardinal 2 ℶ α {\displaystyle 2^{\beth _{\alpha }}} is the result of cardinal exponentiation, and ℶ α + 1 = 2 ℶ α = | 2 A...13 KB (2,227 words) - 02:51, 19 June 2024
questions of cardinal arithmetic (such as the continuum hypothesis), there are still highly nontrivial ZFC theorems about cardinal exponentiation. Shelah constructed...16 KB (1,438 words) - 01:52, 14 April 2024- Continuum function (category Cardinal numbers)power of κ using cardinal exponentiation. Given a cardinal number, it is the cardinality of the power set of a set of the given cardinality. Continuum hypothesis...831 bytes (96 words) - 05:36, 11 March 2024
- λ ℵ 0 = λ {\displaystyle \lambda ^{\aleph _{0}}=\lambda } (see Cardinal exponentiation for an explanation of λ ℵ 0 {\displaystyle \lambda ^{\aleph _{0}}}...62 KB (9,048 words) - 21:05, 25 June 2024
logics, proved that this theory of "pseudo-exponentiation" has a unique model in each uncountable cardinal. Schanuel's conjecture is part of this axiomatisation...10 KB (1,173 words) - 08:45, 7 November 2023- ordinals α β {\displaystyle \alpha ^{\beta }} 1. Cardinal exponentiation 2. Ordinal exponentiation β α {\displaystyle {}^{\beta }\alpha } 1. The set...91 KB (11,511 words) - 21:47, 23 May 2024
Ordinal number (section Initial ordinal of a cardinal)values) are called continuous. Ordinal addition, multiplication and exponentiation are continuous as functions of their second argument (but can be defined...47 KB (6,717 words) - 12:53, 12 July 2024
Arithmetic (section Exponentiation and logarithm)subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can...165 KB (16,364 words) - 23:07, 18 July 2024
Infinity (section Cardinality of the continuum)ever-increasing sequence <1,2,3,...>. 0.999... Aleph number Ananta Exponentiation Indeterminate form Names of large numbers Infinite monkey theorem Infinite...53 KB (6,001 words) - 08:14, 19 July 2024- hierarchy of hyperoperations, used to build addition, multiplication, exponentiation, tetration, etc. It was studied in 1986 in an investigation involving...3 KB (389 words) - 13:27, 27 March 2024
bookkeeping necessary for comparing cardinals of different types. PM define addition, multiplication and exponentiation of cardinals, and compare different definitions...71 KB (9,458 words) - 05:52, 14 July 2024- }(\alpha +\beta )} In particular, S(α) = α + 1. Multiplication and exponentiation are defined similarly. The successor points and zero are the isolated...2 KB (288 words) - 19:08, 18 July 2023
Multiplication (section Exponentiation)all factors are identical, a product of n factors is equivalent to exponentiation: ∏ i = 1 n x = x ⋅ x ⋅ … ⋅ x = x n . {\displaystyle \prod _{i=1}^{n}x=x\cdot...48 KB (6,258 words) - 15:11, 7 July 2024
- "Cardinal Arithmetic", section B, "Addition, Multiplication and Exponentiation", ✸110, "The arithmetical sum of two classes and of two cardinals", p
- therefore, to the commutative, associative, and distributive laws. §4 The Exponentiation of Powers By a "covering of the aggregate N {\displaystyle N} with elements
- Observe that φ(19)=18 and 18|252. 252/18=14. Decompose the exponent then as 218×14=(218)14=1. 6. Use fast exponentiation by squaring: the answer is 3