Aleph Alpha is a German artificial intelligence (AI) startup company founded by professionals with experience as employees of Apple, SAP and Deloitte...

{\displaystyle \aleph _{\alpha }^{\aleph _{\beta }}\leq \aleph _{\alpha }^{\aleph _{\alpha }}\leq (2^{\aleph _{\alpha }})^{\aleph _{\alpha }}=2^{\aleph _{\alpha }\cdot...

derived from the Phoenician letter aleph , which is the West Semitic word for "ox". Letters that arose from alpha include the Latin letter A and the Cyrillic...

and North Arabian. Together with Hebrew aleph, Greek alpha and Latin A, it is descended from Phoenician ʾāleph, from a reconstructed Proto-Canaanite ʾalp...

ℵ 0 , {\displaystyle \beth _{0}=\aleph _{0},} ℶ α + 1 = 2 ℶ α , {\displaystyle \beth _{\alpha +1}=2^{\beth _{\alpha }},} ℶ λ = sup { ℶ α : α < λ } , {\displaystyle...

the set of all integers. More generally, the ℵ α {\displaystyle \aleph _{\alpha }} aleph number notation marks the ordered sequence of all distinct infinite...

fraternities. The letters were chosen to spite the fraternity the Alephs were denied, Alpha Zeta Alpha, by naming their fraternity the Hebrew counterparts. However...

+ , {\displaystyle \aleph _{\alpha ^{+}}=(\aleph _{\alpha })^{+}\,,} if λ is a successor ordinal then ℵ λ {\displaystyle \aleph _{\lambda }} is not a...

colonizing Alpha-Aleph is a source of hope for a better future. As the story progresses, the reader is told that the existence of the planet Alpha-Aleph is a...

{\displaystyle \aleph _{G(\alpha )}} is greater than ℵ α {\displaystyle \aleph _{\alpha }} for each α in the domain of G, and ℵ α {\displaystyle \aleph _{\alpha }}...

  {\displaystyle 0,1,2,3,\ldots ,n,\ldots ;\aleph _{0},\aleph _{1},\aleph _{2},\ldots ,\aleph _{\alpha },\ldots .\ } This sequence starts with the natural...

define ω α {\displaystyle \omega _{\alpha }} as the initial ordinal of the cardinal ℵ α {\displaystyle \aleph _{\alpha }} . The existence of ω 1 {\displaystyle...

Aleph (also known as DOT or 2,5-dimethoxy-4-methylthioamphetamine) is a psychedelic hallucinogenic drug and a substituted amphetamine of the phenethylamine...

anarchy symbol ⟨𐤀⟩: Phoenician aleph, from which the following symbols originally derive: ⟨Α α⟩: Greek letter alpha, from which the following letters...

examples of normal functions are given by the aleph numbers f ( α ) = ℵ α {\displaystyle f(\alpha )=\aleph _{\alpha }} , which connect ordinal and cardinal...

μ ℵ μ − 1 ℵ α . {\displaystyle \aleph _{\mu }^{\aleph _{\alpha }}=\aleph _{\mu }\;\aleph _{\mu -1}^{\aleph _{\alpha }}.} This formula was, together with...

ℵ n − 1 {\displaystyle \aleph _{n-1}} ⁠. If α ≥ ω, the α-th number class has cardinality ⁠ ℵ α {\displaystyle \aleph _{\alpha }} ⁠. Therefore, the cardinalities...

{\displaystyle \aleph _{0}<\aleph _{1}<\aleph _{2}<\ldots .} For each ordinal α {\displaystyle \alpha } , ℵ α + 1 {\displaystyle \aleph _{\alpha +1}} is the...

inaccessible cardinals to be uncountable (in which case ⁠ ℵ 0 {\displaystyle \aleph _{0}} ⁠ is strongly inaccessible). Weakly inaccessible cardinals were introduced...

Aleph Yodh He (איה) was an American professional medical fraternity for Jewish students. It went dormant in 1921 when it merged with Phi Lambda Kappa...

{\displaystyle \aleph _{\alpha +1}=\aleph _{\alpha }^{+}} and for λ an infinite limit ordinal, ℵ λ = ⋃ β < λ ℵ β {\displaystyle \aleph _{\lambda }=\bigcup...

cofinality of ℵ 0 {\displaystyle \aleph _{0}} is ℵ 0 . {\displaystyle \aleph _{0}.} Thus ℵ 0 {\displaystyle \aleph _{0}} is a regular cardinal. The cofinality...

is aleph-one, ℵ 1 . {\displaystyle \aleph _{1}.} If not, there may be other cardinals which are incomparable with aleph-one and larger than aleph-null...

{\displaystyle \omega _{\alpha }} with ℵ α {\displaystyle \aleph _{\alpha }} , except that the notation ℵ α {\displaystyle \aleph _{\alpha }} is used for writing...

Chapters were named in Hebrew alphabetic order, The first chapter was Aleph (Nebraska), the second Beth (Iowa), etc. The sorority published a magazine...

\alpha } , α > ℵ 0 {\displaystyle \textstyle \alpha >\aleph _{0}} : There exist a one-dimensional metric space J α {\displaystyle \textstyle J_{\alpha...

ℵ 0 , ℵ ℵ 0 , ℵ ℵ ℵ 0 , . . . {\displaystyle \aleph _{0},\aleph _{\aleph _{0}},\aleph _{\aleph _{\aleph _{0}}},...} and is therefore singular. If the...

{\displaystyle \aleph _{1}\not \to [\aleph _{1}]_{4}^{2}} and 2 ℵ 0 ↛ [ 2 ℵ 0 ] ℵ 0 2 {\displaystyle 2^{\aleph _{0}}\not \to [2^{\aleph _{0}}]_{\aleph _{0}}^{2}}...

iota) and [u] (Υ, upsilon); the glottal stop consonant /ʔ/ (aleph) was used for [a] (Α, alpha); the pharyngeal /ʕ/ (ʿayin) was turned into [o] (Ο, omicron);...

Alpha Epsilon Pi (ΑΕΠ), commonly known as AEPi, is a college fraternity founded at New York University in 1913. The fraternity has more than 150 active...