The group $\langle 4,3,2 \rangle$ abstractly presented as:
...\langle 3,3,2 \rangle$ as a subgroup of index 2. It occurs as a subgroup of the [[unit quaternion]]s.
612 bytes (88 words) - 20:50, 23 November 2023
The exceptional group $G_4$ or $\langle 3,3,2 \rangle$, abstractly presented as:
...] $A_4$ as quotient by the centre and the [[quaternion group]] of order 8 as a quotient.
764 bytes (115 words) - 20:46, 23 November 2023
The group $\langle 5,3,2 \rangle$ abstractly presented as:
It is finite of order 120. It occurs as a subgroup of the [[unit quaternion]]s.
520 bytes (74 words) - 14:29, 12 November 2023
...s classes of numbers; [[conjunction]], [[disjunction]] and [[implication]] of propositions.
...A \times A$ (as for example division by zero is not defined). Properties of binary operations which occur in many contexts include
1 KB (193 words) - 19:47, 13 November 2016
...uling problems, the problem of minimizing the makespan is as hard to solve as the [[travelling salesman problem]].
309 bytes (46 words) - 12:27, 17 February 2021
...d at the barycentre. Geometrically, the barycentre is at the [[centroid]] of the body.
628 bytes (99 words) - 20:44, 5 December 2023
...ontain elliptic points as well. Thus, an elliptic paraboloid consists only of elliptic points, and is an affine minimal surface.
295 bytes (46 words) - 09:29, 27 June 2014
...a''' is a branch of [[mathematics]]. The term is used in combinations such as [[homological algebra]], [[commutative algebra]], [[Linear-algebra(2)|linea
An [[algebraic system]], consisting of a set with a family of algebraic operations.
788 bytes (106 words) - 11:22, 9 April 2017
A term with a variety of meanings.
...l function]], such as $\exp(x+y) = \exp(x)\exp(y)$ or of a [[power]], such as $x^{yz} = (x^y)^z$.
531 bytes (94 words) - 18:21, 19 December 2014
...hen a computable real number is considered in the framework of some system of constructive mathematics (see [[Constructive analysis|Constructive analysis
388 bytes (57 words) - 17:04, 7 February 2011
...ously with its negation. In the language of propositional calculus the law of contradiction is expressed by
This formula is derivable in classical as well as in intuitionistic [[Constructive propositional calculus|constructive propos
421 bytes (57 words) - 13:51, 30 December 2018
...nly if $P$ is balanced as an $R$-module, projective and finitely generated as an $\mathrm{End}_R P$-module.
646 bytes (112 words) - 20:23, 10 October 2017
...al{A}$-set (Suslin's criterion); and 2) it can be represented as the union of non-intersecting components (Luzin's criterion).
356 bytes (55 words) - 21:57, 19 December 2014
...s are taken as $ h_i $ or as $ m_i $. Thus, let the measurements of trunks of 1000 firs give the following results:
<tr> <td colname="1" style="background-color:white;" colspan="1">number of trunks</td> <td colname="2" style="background-color:white;" colspan="1">100
3 KB (376 words) - 00:30, 11 June 2013
...multiplication $(m,r) \cdot (n,s) = (mn, ms + nr + rs)$ which has $(1,0)$ as a multiplicative identity.
...ra $A$ over a field $K$ is an algebra over $K$ which is unital as a ring. As with rings, any $K$-algebra $A$ can be embedded in a unital $K$-algebra $A^
1 KB (199 words) - 18:38, 13 November 2023
...ignature]]. A Gödelization could be understood as encoding of the elements of $A$ by natural numbers {{Cite|W90}}.
...lon C \longrightarrow A$. More precisely, $\beta=\nu^{-1}$ is the inverse of $\nu$ in this case. For a sensible signature $\Sigma$ and a term-generated
2 KB (241 words) - 07:50, 21 March 2023
...omains in the plane have been constructed with an indecomposable continuum as common boundary.
815 bytes (126 words) - 08:39, 12 April 2014
...ts of two digits" one says the term "12" is used autonymously (as the name of itself).
...d without the quotation marks. Autonymous use of a term merges the meaning of the term with the term itself: it is both the object itself and the name by
2 KB (318 words) - 14:25, 30 December 2018
The same as a [[Degenerate distribution|degenerate distribution]].
...]]; the latter is defined as a [[Measure|measure]] $\mu$ on the Borel sets of $\mathbf R$ such that $\mu(\mathbf R)<1$.
393 bytes (58 words) - 21:48, 11 April 2014
A [[Metric|metric]] $\rho$ which is defined for any two points $x$, $y$ of a [[Metric space|metric space]] that can be connected by a [[rectifiable cu
where $s_\rho$ is the length of the curve in the metric $\rho$. A [[Riemannian metric]] induces an internal
1 KB (231 words) - 12:31, 9 November 2014