Aleph number - Wikipedia
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). [2][a]
ℵ 数 - 香蕉空间
ℵ 数是一列无限基数:ℵ0 ,ℵ1 ,ℵ2 ,…,ℵα ,…,其中 α 取遍所有序数. 如果假定选择公理, 那么这一列基数就是将所有无限基数从小到大排列, 而得到的序列.
What are Aleph numbers intuitively? - Mathematics Stack Exchange
The cardinal number $\aleph_1$ is defined as the cardinality of the set of all countable ordinals, i.e. ordinals of cardinality $\le\aleph_0$. If you believe that that set of countable ordinals exists, then you've got it.
Aleph - Encyclopedia of Mathematics
2021年1月2日 · As symbols, alephs were introduced by G. Cantor to denote the cardinal numbers (i.e., the cardinality) of infinite well-ordered sets. Each cardinal number is some aleph (a consequence of the axiom of choice). However, many theorems about alephs are demonstrated without recourse to the axiom of choice.
elementary set theory - Could someone explain aleph numbers ...
There exists an $\aleph_\alpha$ for every ordinal number $\alpha$. If every set can be well-ordered --- a proposition equivalent to the axiom of choice --- then every infinite cardinality is one of these. $2^{\aleph_0}$ is the cardinality of the set of …
Aleph number - WikiMili, The Best Wikipedia Reader
2024年9月21日 · 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). [2] [lower-alpha 1]
Aleph -- from Wolfram MathWorld
3 天之前 · The set theory symbol (aleph) for the cardinal number of a well-orderable infinite set.
Cardinality of important sets - Department of Mathematics at UTSA
2021年11月11日 · 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 and are named after the symbol he used to denote them, the Hebrew letter aleph ( ).
阿列夫数-数学百科
在 集合论 中， 阿列夫数 或 艾礼富数 是一连串 超穷基数。 其标记符号为 ℵ （由 希伯来字母א (aleph)演变而来）加角标表示。 可数集 （包括 自然数）的势标记为 ，下一个较大的 势 为 ，再下一个是 ，以此类推。 一直继续下来，便可以对任一 序数 α 定义一个基数 。 这一概念来自于 康托尔，他定义了势，并认识到无穷集合是可以有不同的势的。 阿列夫数与一般在代数与微积分中出现的 无限 (∞) 不同。 阿列夫数用来衡量集合的大小，而无限只是在 极限 的写法中出现，或是定 …
aleph numbers - PlanetMath.org
2018年2月8日 · The aleph numbers are infinite cardinal numbers defined by transfinite recursion, as described below. They are written ℵ α, where ℵ is aleph, the first letter of the Hebrew alphabet, and α is an ordinal number. Sometimes we write ω α instead of ℵ …
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