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Everything about Aleph number
Infinite cardinal number
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph (ℵ). Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Aleph numberA 5-minute orientation
- Skim a recent paper: Revised version of “Non-trivial automorphisms of $${\mathscr {P}}({\mathbb {N}})/[{\mathbb {N}}]^{<\aleph _0}$$ from variants of small dominating number”Influential work since 2022
- Pick up a classic book: Foundation's EdgeThe most-reprinted book on the subject
- Go sideways: CofinalityA closely related topic
- Go sideways: Beth numberA closely related topic
📖 Definitions
Noun Any of a sequence of numbers used to represent the cardinality of infinite sets, denoted by the Hebrew letter aleph.
🏆 Landmark papers (most cited)
- No matching papers found.
🆕 Influential since 2022
📚 Books worth reading
Foundation's EdgeIsaac Asimov · 1977- 📕Hebrew Scripture JournalAleph Publishing · 2021
The first Hebrew bookArnold, Thomas Kerchever · 1851- 📕All after AlephFolayan Zheng · 2023
Libera Aleph vel cxiAleister Crowley · 1962- 📕Hebrew Aleph-Bet Memorization Course for Beginners : Memorizing the Aleph-Bet, the Ten Commandments, a Hebrew Pictograph, the Number Sequence, and Numerical Values from 1-400Malkiyah URIEL · 2020
- 📕Liber Aleph Vel CXI
- 📕[Papers on transfinite numbers, divergent series, etc.]Henri Eyraud · 1950
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Cofinality In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets…
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- Cardinal number In mathematics, a cardinal number, or cardinal for short, is a kind of number that measures the cardinality of a set, i.e., how many elements there are…
- Uncountable set In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely…
- Continuum hypothesis In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states:…
- Ordinal number In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite…
- Spectrum of a theory In model theory, a branch of mathematical logic, the spectrum of a theory is given by the number of isomorphism classes of models in various cardinalities…
- Regular cardinal In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa }…