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- ...absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110010/b1100101.png" /> (cf. [[Runge–Kutta method|Runge–Kutta met ...absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110010/b1100102.png" /> satisfies a one-sided Lipschitz condition11 KB (1,517 words) - 17:23, 7 February 2011
- ...ent if they are fibrewise homotopic. No method of consistently defining $( B _ { n } , \phi _ { n } )$-structures for equivalent fibrations exists, beca ...old $M ^ { n }$ with a fixed $( B , \phi )$-structure on it is called a $( B , \phi )$-manifold.3 KB (457 words) - 17:02, 1 July 2020
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- ...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 is1 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 of2 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