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American manufacturer of 3D printers
Aleph Objects, Inc. was a small manufacturing company based in Loveland, Colorado. Their business model focused around the development of open-source
Aleph_Objects
Infinite cardinal number
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.
Aleph_number
1945 short story by Jorge Luis Borges
"The Aleph" (Spanish: El Aleph) is a short story by Argentine writer and poet Jorge Luis Borges. First published in September 1945, it was reprinted in
The_Aleph_(short_story)
Open source firmware for 3D printers
project. Early machines included the Ultimaker 1, the TAZ series by Aleph Objects and the Prusa i3 by Prusa Research. By 2018 manufacturers had begun
Marlin_(firmware)
Proposition in mathematical logic
is equivalent to the following equation in aleph numbers: 2 ℵ 0 = ℵ 1 {\displaystyle 2^{\aleph _{0}}=\aleph _{1}} , or even shorter with beth numbers:
Continuum_hypothesis
3D printing process that melts thermoplastic material from a spool of filament
prices in the US$2,000 range. The LulzBot 3D printers manufactured by Aleph Objects are another example of an open-source application of fused deposition
Fused_filament_fabrication
Los Angeles, California, USA Airwolf 3D – Costa Mesa, California, USA Aleph Objects – Loveland, Colorado, USA – (Lulzbot printers), (owned by FAME 3D) Bambu
List of 3D printer manufacturers
List_of_3D_printer_manufacturers
Japanese cult and terrorist organization
Aleph (Japanese: アレフ, Hepburn: Arefu), better known by their former name Aum Shinrikyo (オウム真理教, Ōmu Shinrikyō; lit. 'religion of Aum Supreme Truth'),
Aum_Shinrikyo
Size of a set in mathematics
individual objects they contain, which may be infinite. The concept is understood through one-to-one correspondences between sets. That is, if their objects can
Cardinality
extruder, provide the filament for RepRaps LulzBot – 3D printer design by Aleph Objects; is Respects Your Freedom certified by the Free Software Foundation
List of open-source hardware projects
List_of_open-source_hardware_projects
Size of a possibly infinite set
denoted by ℵ 0 {\displaystyle \aleph _{0}} (aleph-null), since it is the smallest aleph number. The properties of other aleph numbers and of infinite cardinal
Cardinal_number
Jewish humanitarian organization
The Aleph Institute is an American non-profit organization affiliated with the Chabad-Lubavitch movement that provides support services to the approximately
Aleph_Institute
First letter of the Greek alphabet
numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph ⟨𐤀⟩, whose name comes from the West Semitic word for 'ox'. Letters that
Alpha
Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example
Mathematical_object
Video game series
Voice chat can be used to communicate with other players. Using the modern Aleph One engine, games can be played over TCP/IP networks (LAN or Internet),
Marathon_(series)
Infinite Cardinal number
beth. The beth numbers are related to the aleph numbers ( ℵ 0 , ℵ 1 , … {\displaystyle \aleph _{0},\aleph _{1},\dots } ), but unless the generalized
Beth_number
4th-century handwritten Bible copy in Greek
and the Shepherd of Hermas included. It is designated by the siglum א [Aleph] or 01 in the Gregory-Aland numbering of New Testament manuscripts, and
Codex_Sinaiticus
Infinite set that is not countable
equal to ℵ 0 {\displaystyle \aleph _{0}} (aleph-null). The set X has cardinality strictly greater than ℵ 0 {\displaystyle \aleph _{0}} . The first three of
Uncountable_set
Blender Foundation, Google, NASA, Valve, Sony Interactive Entertainment, Aleph Objects, Nvidia, Intel, AMD EdX Massive open online courses Massachusetts Institute
Open_coopetition
{\displaystyle \aleph _{0}} -presentable object is called finitely presentable. In the category Set of all sets, the finitely presentable objects coincide with
Accessible_category
is a very large space (of cardinality ℵ ω ℵ 0 {\displaystyle \aleph _{\omega }^{\aleph _{0}}} ). Zoltán Balogh gave the first ZFC construction of a small
Dowker_space
First letter of the Latin alphabet
letter's pronunciation in open syllables. The earliest known ancestor of A is aleph—the first letter of the Phoenician alphabet—where it represented a glottal
A
Smallest cardinal strictly greater in size than another cardinal
{\displaystyle \aleph _{\alpha +1}=\aleph _{\alpha }^{+}} and for λ an infinite limit ordinal, ℵ λ = ⋃ β < λ ℵ β {\displaystyle \aleph _{\lambda }=\bigcup
Successor_cardinal
Type of cardinal number in mathematics
ℵ 0 {\displaystyle \aleph _{0}} , ℵ 1 {\displaystyle \aleph _{1}} , ℵ 2 {\displaystyle \aleph _{2}} , ℵ 3 {\displaystyle \aleph _{3}} , and so on. Its
Regular_cardinal
Collection of mathematical objects
foundational objects whose behavior is described by axioms modeled on intuition about collections, and then essentially all other mathematical objects are rigorously
Set_(mathematics)
Concept in philosophy and set theory
describe these objects. In his Grundlagen 1883, prior to the discovery of any of these paradoxes, Cantor noticed these kinds of objects (universe of sets
Absolute_infinite
Mathematical symbol representing infinity
other kinds of infinite values. For example, ℵ 0 {\displaystyle \aleph _{0}} (aleph-nought) denotes the smallest infinite cardinal number (representing
Infinity_symbol
that codes more than ℵ 1 {\displaystyle \aleph _{1}} reals, without changing the value of ℵ 1 {\displaystyle \aleph _{1}} . Formally, let P be a partially
Generic_filter
Argentine writer (1899–1986)
literature. His best-known works, Ficciones (transl. Fictions) and El Aleph (transl. The Aleph), published in the 1940s, are collections of short stories exploring
Jorge_Luis_Borges
Intersection of Set Theory and General Topology
is a very large space (of cardinality ℵ ω ℵ 0 {\displaystyle \aleph _{\omega }^{\aleph _{0}}} ) and is generally not well-behaved. Zoltán Balogh gave
Set-theoretic_topology
Concept in mathematics
associative) finite products and a strict identity-on-objects functor I : ℵ 0 op → L {\displaystyle I:\aleph _{0}^{\text{op}}\rightarrow L} preserving finite
Lawvere_theory
Numerological practice of reading a word or phrase as a number
standard values of the resulting string. For example, the letter aleph is spelled aleph lamed peh [אלף], giving it a value of 1 + 30 + 80 = 111 {\displaystyle
Gematria
Mathematical concept
concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity
Infinity
Branch of mathematics that studies sets
studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch
Set_theory
Short story by Jorge Luis Borges
writer and poet Jorge Luis Borges. It is one of the stories in the book The Aleph and Other Stories, first published in 1949, and revised by the author in
The_Zahir
used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
System of symbolic representation
alphabets are also used sporadically, such as the Hebrew ℵ {\displaystyle \aleph } , Cyrillic Ш, and Hiragana よ. Uppercase and lowercase letters are considered
Mathematical_notation
Mathematician (1845–1918)
then its cardinality is an aleph since the alephs are the cardinals of well-ordered sets. If a set's cardinality is an aleph, then it can be well-ordered
Georg_Cantor
1947 short story by Jorge Luis Borges
de Buenos Aires and republished in Borges's short story collection The Aleph in 1949. It is based on the Greek myth of Theseus and the Minotaur and is
The_House_of_Asterion
Measurement tool
Gerson and the Cross Staff Revisted". Aleph. 11 (2): 365–385. doi:10.2979/aleph.11.2.365. JSTOR 10.2979/aleph.11.2.365.pdf?refreqid=excelsior:a08ab1
Jacob's_staff
Number representing a continuous quantity
set of all natural numbers, denoted ℵ 0 {\displaystyle \aleph _{0}} and called aleph-zero or aleph-nought. The cardinality of the continuum equals the cardinality
Real_number
Philosophical theory
with their own cardinality: finite, ℵ 0 {\displaystyle \aleph _{0}} and ℵ 1 {\displaystyle \aleph _{1}} . In practice, the terms "good" and "bad" apply
Science_of_value
Tractate of the Talmud
Steinsaltz, Rabbi Adin Even-Israel; Society, The Aleph (2014-04-01). "The Aleph Society- Let My People Know". The Aleph Society. Retrieved 2024-06-25. "Torah Texts
Beitza
number of some species is not specified due to inadequate information. ALEPH-1 is the mission, Beresheet 2 is the spacecraft. "Apollo 11 Mission Overview
List of species that have landed on the Moon
List_of_species_that_have_landed_on_the_Moon
1998 book by Leonard Shlain
historical periods, such as Image vs. Word; Hunters vs. Gatherers; and Aleph vs. Bet. Criticism has been leveled at the book for multiple reasons. One
The Alphabet Versus the Goddess
The_Alphabet_Versus_the_Goddess
Generalization of "n-th" to infinite cases
written ℵ α {\displaystyle \aleph _{\alpha }} . For example, the cardinality of ω0 = ω is ℵ 0 {\displaystyle \aleph _{0}} , which is also the cardinality
Ordinal_number
Script used to write the Greek language
for [i] (Ι, iota) and [u] (Υ, upsilon); the glottal stop consonant /ʔ/ (aleph) was used for [a] (Α, alpha); the pharyngeal /ʕ/ (ʿayin) was turned into
Greek_alphabet
Paradox in set theory
is an arbitrary collection of objects, absolutely no restriction being placed on the nature and number of these objects, the elements of the set in question
Russell's_paradox
2001 video game
Aleph, which is guarded by the town of Vale at the mountain's base. In the game's prologue, Saturos and Menardi lead a raiding party into Mt. Aleph to
Golden_Sun_(video_game)
2009 role-playing game
will to create a united utopia. Key items are the Cosmic Eggs, objects created by Mem Aleph that can reshape the world when combined with the core of the
Shin Megami Tensei: Strange Journey
Shin_Megami_Tensei:_Strange_Journey
Model theory concept
{\displaystyle \textstyle I(T,\aleph _{\xi })<\beth _{\omega _{1}}(|\xi |+\aleph _{0})} for all ordinals ξ (See Aleph number and Beth number for an explanation
Spectrum_of_a_theory
{\displaystyle \aleph _{1}} -saturated models of T, together with elementary substructure, is an AEC with Löwenheim–Skolem number 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}}
Abstract_elementary_class
Measure of algorithmic complexity
an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as
Kolmogorov_complexity
Model for mathematical theories
For example, an ultrapower model of the hyperreals is ℵ 1 {\displaystyle \aleph _{1}} -saturated, meaning that every descending nested sequence of internal
Saturated_model
Mathematical set that can be enumerated
{\displaystyle |S|} is less than or equal to ℵ 0 {\displaystyle \aleph _{0}} (aleph-null), the cardinality of the set of natural numbers N {\displaystyle
Countable_set
Standard system of axiomatic set theory
set theorists of the time, notably the cardinal number aleph-omega ( ℵ ω {\displaystyle \aleph _{\omega }} ) and the set { Z 0 , P ( Z 0 ) , P ( P ( Z
Zermelo–Fraenkel_set_theory
Type of infinite number in set theory
(1930); in the latter they were referred to along with ℵ 0 {\displaystyle \aleph _{0}} as Grenzzahlen (English "limit numbers"). Every strongly inaccessible
Inaccessible_cardinal
Northwest Semitic language
language". The Guardian. ISSN 0261-3077. Retrieved 5 August 2024. "'Kometz Aleph – Au': How many Hebrew speakers are there in the world?". Nachman Gur for
Hebrew_language
American former pornographic actress (born 1988)
2009. The same year, Grey also contributed vocals to the Current 93 album Aleph at Hallucinatory Mountain. In 2010, aTelecine released its first album,
Sasha_Grey
Type of accumulation point
of S. Thus "condensation point" is synonymous with " ℵ 1 {\displaystyle \aleph _{1}} -accumulation point". If S = (0,1) is the open unit interval, a subset
Condensation_point
Zodiac constellation straddling the celestial equator
consequently it was represented by the first letter in their alphabet, Aleph. In Greek mythology, Taurus was identified with Zeus, who assumed the form
Taurus_(constellation)
Symbol that represents an idea or concept
language, such as the adaptation of the logogram for ʾālep 'ox' as the letter aleph representing the initial glottal stop. However, some logograms still meaningfully
Ideogram
Theorem in set theory
index set I is the natural numbers, yields the sum ℵ 0 {\displaystyle \aleph _{0}} for both sides, and we have an equality. If κ {\displaystyle \kappa
Kőnig's_theorem_(set_theory)
Writing system used c. 1050 to 146 BC
list of inscribed objects from different time periods that together illustrate the evolution of the Phoenician alphabet. The objects are Lebanese state
Phoenician_alphabet
infinite. Aleph-null: ℵ0, the smallest infinite cardinal, and the cardinality of N {\displaystyle \mathbb {N} } , the set of natural numbers Aleph-one: ℵ1
List_of_numbers
Japanese anime television series
King Aleph. Aleph's brother in-law, Guwaru the Ziarc, opposes him and has plans to seize the throne. When Hat enters the Underworld, Guwaru and Aleph are
Magical_Hat
Two sets with a small overlap
definition of disjoint sets; the case of κ = ℵ 0 {\displaystyle \kappa =\aleph _{0}} is simply the definition of almost disjoint given above, where the
Almost_disjoint_sets
1972 novella by Frederik Pohl
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 hoax
The_Gold_at_the_Starbow's_End
Theorem in set-theoretic geometry
many pieces as there are real numbers (that is, 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} pieces), so that each piece is equidecomposable with two pieces to
Banach–Tarski_paradox
Ancient Egyptian goddess
second t marks a feminine ending but usually was not pronounced, and the aleph ꜣ () may have moved to a position before the accented syllable, ꜣbst. By
Bastet
Fifth letter of many Semitic alphabets
a-vowel, usually that of qamatz ( ָ ), and in this sense functions like Aleph, Vav, and Yud as a mater lectionis, indicating the presence of a long vowel
He_(letter)
Short story by Jorge Luis Borges
Aires in April 1947 and appears in the 1949 short story collection The Aleph. The story follows Aurelian and John of Pannonia, who compete with one another
The_Theologians
System of mathematical set theory
infinite set, that is, of a set whose cardinality is ℵ 0 {\displaystyle \aleph _{0}} . Even if GST did afford a countably infinite set, GST could not prove
General_set_theory
Plant mentioned in the Bible
Rabbi Jonah ibn Janah (Sefer HaShorashim - Book of the Roots, s.v. אזב - aleph, zayn, bet), Maimonides (in his Mishnah Commentary, Nega'im 14:6) and Nathan
Ezov
Construction in category theory
"glue together" several related objects, the precise gluing process being specified by morphisms between the objects. Inverse limits can be defined in
Inverse_limit
Proof in set theory
denoted by c {\displaystyle {\mathfrak {c}}} or 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} . An injection from T to R is given by mapping binary strings in
Cantor's_diagonal_argument
Indian historian (born 1931)
Through History, 2014; Aleph, ISBN 93-83064-01-3 Which of Us are Aryans?: Rethinking the Concept of Our Origins. 2019, Aleph. ISBN 978-93-88292-38-2
Romila_Thapar
As simple a model as possible, in model theory
{\displaystyle T} of cardinality max ( κ , ℵ 0 ) . {\displaystyle \max(\kappa ,\aleph _{0}).} Therefore, no prime model of T {\displaystyle T} can have larger
Prime_model
Japanese manga series by Osamu Nishi
Prophecy instead of a rank badge, so he was placed in the lowest rank: Aleph (Rank 1). Also, Iruma accidentally made his homeroom teacher, Kalego, his
Welcome to Demon School! Iruma-kun
Welcome_to_Demon_School!_Iruma-kun
Mathematical treatise by Euclid
Elements". Aleph: Historical Studies in Science and Judaism. 21 (1). Indiana University Press: 123–148. doi:10.2979/aleph.21.1.0123. JSTOR 10.2979/aleph.21.1
Euclid's_Elements
German mathematician (1868–1942)
α = ℵ μ ℵ μ − 1 ℵ α . {\displaystyle \aleph _{\mu }^{\aleph _{\alpha }}=\aleph _{\mu }\;\aleph _{\mu -1}^{\aleph _{\alpha }}.} This formula was, together
Felix_Hausdorff
Numbers significantly larger than those used regularly
which quantifies permutations of a fixed set of objects, grows superexponentially as the number of objects increases. Stirling's formula provides a precise
Large_numbers
Set-theoretic concept
U ) {\displaystyle \mathbf {c} (U)} is either zero, ℵ 0 {\displaystyle \aleph _{0}} , or strongly inaccessible. Assuming it is uncountable, it is a strong
Grothendieck_universe
they remained so in Greek. Since the names of the letters ʼāleph and hē were pronounced [alepʰ] and [e] by the Greeks, with initial vowels due to the silent
History_of_the_Greek_alphabet
Method of deriving conclusions
for this modification is the idea that proofs should demonstrate that an object exists or can be constructed, not merely that its nonexistence would lead
Rule_of_inference
or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship such objects have with physical reality
Philosophy_of_mathematics
Area of mathematical logic
{\displaystyle \lambda ^{\aleph _{0}}=\lambda } (see Cardinal exponentiation for an explanation of λ ℵ 0 {\displaystyle \lambda ^{\aleph _{0}}} ). T is λ {\displaystyle
Model_theory
Mathematical set containing all objects
In set theory, a universal set is a set that contains all of the objects in the theory, including itself. In set theory as usually formulated, it can
Universal_set
a mathematical object whose main component is a set, it means that the cardinality of the set is less than ℵ 0 {\displaystyle \aleph _{0}} . frequently
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
American space technology company
Emiliano Kargieman and Gerardo Richarte. Satellogic began launching their Aleph-1 constellation of ÑuSat satellites in May 2016 and has, as of September
Satellogic
Geometrical figure
"and" (introduced by Johannes Widmann in the late 15th century). The letter Aleph is cross-shaped in Aramaic and paleo-Hebrew. Egyptian hieroglyphs with cross-shapes
Cross
Word used with a noun to indicate the type of reference being made by the noun
(shalma), the peace Note: Aramaic is written from right to left, so an Aleph is added to the end of the word. ם becomes מ when it is not the final letter
Article_(grammar)
Hebrew book on Jewish mysticism
shin" Aspirates, such as Aleph, which holds a position between the mutes and sibilants, and is designated as the "airy Aleph, which holds the balance
Sefer_Yetzirah
1993 video game
News. Retrieved July 18, 2024. "Aleph One: Pathways Into Darkness - A full port of the 1993 mac game to the Aleph One engine". Indie Retro News. February
Pathways_into_Darkness
{\displaystyle \aleph _{1}} -dense if every open interval contains ℵ 1 {\displaystyle \aleph _{1}} -many elements of X. Whether all ℵ 1 {\displaystyle \aleph _{1}}
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
System of mathematical set theory
Zermelo set theory are stated for objects, some of which (but not necessarily all) are sets, and the remaining objects are urelements and not sets. Zermelo's
Zermelo_set_theory
Numbers Authority. Retrieved 2024-11-12. "Open Microscopy Environment Remote Objects Documentation — Server Security". Open Microscopy Environment. Retrieved
List of TCP and UDP port numbers
List_of_TCP_and_UDP_port_numbers
Magic involving communication with the deceased
18:9–12. cf. Tanakh, Torah, Vayikra 20:27. cf. Tanakh, Nevi'im, Shmu'el Aleph 28:3–25 Archived 2012-05-09 at the Wayback Machine. William Godwin (1876)
Necromancy
Retrieved 21 June 2020. Krebs, Gunter (12 June 2020). "ÑuSat 1, ..., 98 (Aleph-1 1, ..., 98)". Gunter's Space Page. Archived from the original on 3 December
2020_in_spaceflight
Technique invented by Paul Cohen for proving consistency and independence results
universe might contain many new real numbers (at least ℵ 2 {\displaystyle \aleph _{2}} of them), identified with subsets of the set N {\displaystyle \mathbb
Forcing_(mathematics)
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