aleph-null

aleph-null
The first of the transfinite cardinal numbers; corresponds to the number of positive integers, also called natural numbers. Georg Cantor showed that even all the rational numbers could be put in one-to-one correspondence with them, and are therefore countable, enumerable or denumerable.
Syn: aleph-naught, aleph-zero, <sub dir="ltr">0</sub>א
See Also: aleph-one

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  • aleph-null — [ä′lifzir′ōä′lifnul′] n. Math. in the theory of sets, the smallest infinite cardinal number; the cardinal number of the set of all positive integers: symbol, (א0): also called aleph zero [ä′lifzir′ō] …   English World dictionary

  • Aleph null — In der Mathematik verwendet man den aus der Mengenlehre von Cantor stammenden Begriff der Mächtigkeit oder Kardinalität, um den für endliche Mengen verwendeten Begriff der „Anzahl der Elemente einer Menge“ auf unendliche Mengen zu verallgemeinern …   Deutsch Wikipedia

  • aleph-null — noun the smallest infinite integer • Syn: ↑aleph nought, ↑aleph zero • Hypernyms: ↑large integer * * * | ̷ ̷(ˌ) ̷ ̷| ̷ ̷ noun also aleph zero | ̷ ̷(ˌ) ̷ ̷ˈ ̷ ̷(ˌ) ̷ ̷ …   Useful english dictionary

  • aleph-null — /ah lif nul /, n. Math. the cardinal number of the set of all positive integers; the smallest transfinite cardinal number. Also called aleph zero /ah lif zear oh/. [1905 10] * * * …   Universalium

  • aleph-null — a′leph null′ n. math. the cardinal number of the set of all positive integers; the smallest transfinite cardinal number. Also called a′leph ze′ro • Etymology: 1905–10 …   From formal English to slang

  • aleph-null — noun Date: circa 1909 the number of elements in the set of all integers which is the smallest transfinite cardinal number …   New Collegiate Dictionary

  • Aleph (disambiguation) — * Aleph or Alef is the first letter of the Semitic abjads descended from Proto Canaanite, Arabic alphabet, Phoenician alphabet, Hebrew alphabet, Syriac alphabet.Named after the letterPeople* Aleph (musician), an Italo disco artist and alias of… …   Wikipedia

  • Aleph — Aleph,   Anfangsbuchstabe des hebräischen Alphabets (geschrieben ). Er bezeichnet einen konsonantischen Kehllaut. In der Mathematik Bezeichnung für die Kardinalzahl (die Mächtigkeit) einer wohl geordneten Menge. Die kleinste transfinite… …   Universal-Lexikon

  • Aleph number — In the branch of mathematics known as set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph (aleph).The… …   Wikipedia

  • aleph-zero — noun the smallest infinite integer • Syn: ↑aleph null, ↑aleph nought • Hypernyms: ↑large integer * * * noun see aleph null …   Useful english dictionary

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