...n which order is significant; $(a,b)$ is not the same as $(b,a)$ unless $a=b$. Equality between ordered pairs is defined by
(a,b) = (c,d) \ \Leftrightarrow \ a=c \wedge b=d \ .
662 bytes (112 words) - 11:56, 23 November 2023
...$AB$. The expressions $A$ and $B$ are called the conjunctive terms of $A\&B$. The normal usage of the conjunction in mathematical logic corresponds to
|$A$||$B$||$A\&B$
623 bytes (106 words) - 07:28, 12 August 2014
...B$ has the property that for every $a \in A$ there is $b \in B$ such that $b \le a$.
451 bytes (77 words) - 20:25, 20 November 2023
$$I_x(a,b)=\frac1{B(a,b)}\int\limits_0^xt^{a-1}(1-t)^{b-1}dt,$$
$$0\leq x\leq1,\quad a>0,\quad b>0,$$
2 KB (393 words) - 15:50, 31 March 2017
...triangle in the Euclidean plane with sides $a,b,c$ and opposite angles $A,B,C$, respectively, the equalities
$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$$
671 bytes (114 words) - 14:29, 19 March 2014
...ments $A$ and $B$ are called the disjunctive terms of the statement $A\lor B$. The meaning of the disjunction can be expressed by the following [[Truth
|$A$||$B$||$A\lor B$
573 bytes (98 words) - 07:30, 12 August 2014
* $|a|-|b|\leq |a+b| \leq |a| + |b|$,
* $|a|-|b|\leq |a-b| \leq |a| + |b|$,
752 bytes (129 words) - 16:51, 30 November 2014
...triple product''' or ''[[mixed product]]'' of vectors $\mathbf{a},\mathbf{b},\mathbf{c}$ is
...= \mathbf{a} \times \mathbf{b} \cdot \mathbf{c} = \mathbf{a} \cdot \mathbf{b} \times \mathbf{c}\ ;
1 KB (176 words) - 19:37, 6 December 2023
...ied to $b$. Then $G \mapsto g$ defines a map from $(A^B)^C \rightarrow A^{B \times C}$. These two correspondences are mutually inverse.
\mathfrak{a}^{\mathfrak{b}\mathfrak{c}} = (\mathfrak{a}^{\mathfrak{b}})^{\mathfrak{c}} \ .
2 KB (289 words) - 11:59, 23 November 2023
...be a continuous mapping and let $m < n$. Then there is an $x \in \partial B$ such that $\phi(x) = \phi(-x)$.
The original version (K. Borsuk, 1933) was for $B = D^n$, the $n$-dimensional ball in $\mathbf{R}^n$, $n = m$. The result is
1 KB (208 words) - 20:43, 19 January 2016
...ich contains the end points, i.e. consists of the points $x$, $a\leq x\leq b$.
...increasingly popular) alternative $]a,b[$ to denote the open interval $a<x<b$.
583 bytes (98 words) - 13:30, 9 April 2014
...taken to be true if $A$ is true and $B$ is false, or if $A$ is false and $B$ is true. In the remaining cases it is taken to be false. Thus, the exclusi
\[A\mathbin{\dot\lor}B\Leftrightarrow(A\lor B)\mathbin\&\neg(A\land B).\]
500 bytes (90 words) - 13:49, 30 December 2018
...such that if $ a \leq b $ (where $ a,b \in A $), then $ \phi(a) \geq \phi(b) $. The dual concept to an antitone mapping is an [[isotone mapping]].
293 bytes (51 words) - 02:57, 9 January 2017
...\phi : A \otimes_{k} B \to \Omega$ that maps the tensor product $a \otimes b$ to $ab \in \Omega$.
347 bytes (59 words) - 21:46, 22 October 2017
...ct of $A$ and $B$ can be defined without assuming in advance that $A$ and $B$ are subgroups of a certain group $C$.
857 bytes (151 words) - 21:01, 10 January 2017
...$, where $[a]$ is the class containing the element $a$, if $a\triangleleft b$. For examples and references see [[Partially ordered set]].
...me writers use the notation $a||b$ to indicate that neither $a\leq b$ nor $b\leq a$ holds.
3 KB (573 words) - 12:32, 6 February 2021
...tarrow B $ such that $ a < b $ in $ A $ implies $ \phi(a) > \phi(b) $ in $ B $ (and similarly for the inverse).
414 bytes (61 words) - 02:54, 9 January 2017
...c$, that is, for each $a\in A$ there is at most one $b\in A$ such that $(a,b)\in R$. Thus, $R$ determines a function (perhaps not defined everywhere) on
...B$ between sets $A$ and $B$ such that $(a,b)\in R$ and $(a,c)\in R$ imply $b=c$.
728 bytes (135 words) - 07:00, 1 May 2016
$$A\supset(\neg A\supset B).$$
...of intuitionistic propositional calculus is formulated as follows. Let $A,B,C$ be arbitrary formulas in the logical language considered. The axioms of
2 KB (271 words) - 21:33, 15 December 2015
...he first). Then the set of those elements of $A$ that are not elements of $B$ is called the difference of these sets.
The difference between two sets $A$ and $B$ is denoted by $A\setminus B$.
660 bytes (113 words) - 05:43, 22 April 2023