Aleph Objects, Inc. was a small manufacturing company based in Loveland, Colorado. Their business model focused around the development of open-source...

introduced, which are often denoted with the Hebrew letter ℵ {\displaystyle \aleph } (aleph) marked with subscript indicating their rank among the infinite cardinals...

In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets....

"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...

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:...

Aleph (Japanese: アレフ, Hepburn: Arefu), better known by their former name Aum Shinrikyo (オウム真理教, Oumu Shinrikyō; lit. 'religion of Aum Supreme Truth')...

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...

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...

extruder, provide the filament for RepRaps LulzBot – 3D printer design by Aleph Objects; is Respects Your Freedom certified by the Free Software Foundation...

Los Angeles, California, USA Airwolf 3D – Costa Mesa, California, USA Aleph Objects – Loveland, Colorado, USA – (Lulzbot printers), (owned by FAME 3D) Bambu...

The Aleph Institute is an American non-profit organization affiliated with the Chabad-Lubavitch movement that provides support services to the approximately...

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),...

Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example...

^{\infty }|={\mathfrak {c}}^{\aleph _{0}}=\left(2^{\aleph _{0}}\right)^{\aleph _{0}}=2^{(\aleph _{0}\cdot \aleph _{0})}=2^{\aleph _{0}}={\mathfrak {c}}=|\mathbb...

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...

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...

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...

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...

{\displaystyle \aleph _{0}} -presentable object is called finitely presentable. In the category Set of all sets, the finitely presentable objects coincide with...

Blender Foundation, Google, NASA, Valve, Sony Interactive Entertainment, Aleph Objects, Nvidia, Intel, AMD EdX Massive open online courses Massachusetts Institute...

|=\aleph _{0}} are called countable sets; these are either finite sets or countably infinite sets (sets of cardinality ℵ 0 {\displaystyle \aleph _{0}}...

with their own cardinality: finite, ℵ 0 {\displaystyle \aleph _{0}} and ℵ 1 {\displaystyle \aleph _{1}} . In practice, the terms "good" and "bad" apply...

infinite entities taken as objects per se, other notations are typically used. For example, ℵ 0 {\displaystyle \aleph _{0}} (aleph-nought) denotes the smallest...

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...

concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity...

used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols...

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...

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

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...

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...