a+b=b+a,\quad \text{ and } \quad ab=ba.
...e law of commutativity) if in the given algebraic system the identity $a*b=b*a$ holds.
427 bytes (66 words) - 22:17, 26 October 2014
|$A$||$B$||$A\downarrow B$
...junction $A\lor B$ is equivalent to $(A\downarrow B)\downarrow(A\downarrow B)$. This arrow was introduced by C. Peirce.
1 KB (194 words) - 12:27, 12 August 2014
$$A\supset(B\supset A),\quad(A\supset(B\supset C))\supset((A\supset B)\supset(A\supset C)),$$
$$A\&B\supset A,\quad A\&B\supset B,\quad A\supset(B\supset A\&B),$$
2 KB (246 words) - 08:00, 12 August 2014
''of an arithmetical fraction $a/b$''
...raction. The denominator of an algebraic fraction $A/B$ is the expression $B$ (see [[Fraction|Fraction]]).
340 bytes (49 words) - 09:49, 15 April 2014
...$a$ and $b$ and including the end points $a$ and $b$. It is denoted by $[a,b]$. See also [[Interval and segment|Interval and segment]].
238 bytes (42 words) - 13:25, 9 April 2014
''of an arithmetic fraction $a/b$''
...is used to make up the fraction. The numerator of an algebraic fraction $A/B$ is the expression $A$ (cf. [[Fraction|Fraction]]).
238 bytes (42 words) - 09:50, 15 April 2014
...of $a$ and $b$. If this number $n$ can be chosen independently of $a$ and $b$, then $G$ is called an Engel group of finite class $n$. The class of Engel
...pringer (1982)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> B. Huppert, "Finite groups" , '''3''' , Springer (1982)</TD></TR></table>
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...ment $x\in P$ such that $a<x<b$: the [[Interval and segment|interval]] $[a,b]$ is an ''atomic'' or ''[[elementary interval]]''.
351 bytes (59 words) - 07:37, 24 January 2016
''$B$-function, Euler $B$-function, Euler integral of the first kind''
B(p,q) = \int_0^1 x^{p-1}(1-x)^{q-1} \rd x.
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|$A$||$B$||$A|B$
...A|A$; the [[Disjunction|disjunction]] $A\lor B$ of two assertions $A$ and $B$ is expressed as:
2 KB (249 words) - 17:56, 29 November 2014
''of vectors $\mathbf{a},\mathbf{b},\mathbf{c}$''
...product]] of the vector $\mathbf{a}$ by the [[vector product]] of $\mathbf{b}$ and $\mathbf{c}$:
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...cture(2)|Structure]]), it follows that $A$ is [[existentially closed]] in $B$.
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...tent to a subset of the other), then there is a bijection between $A$ and $B$ (they are [[equipotent sets]]).
...{b}$ and $\mathfrak{b} \le \mathfrak{a}$ implies $\mathfrak{a} = \mathfrak{b}$.
1,006 bytes (155 words) - 19:36, 17 November 2023
$$x=a\cos t,\quad y=\pm\sqrt{b^2-a^2\sin^2t},\quad z=a\sin t,\quad b\geq a,$$
...e $a$ and $b$ are the radii of the cylinders and $t$ is a parameter. If $a=b$, the bicylindrics is a pair of congruent ellipses.
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''of a group $A$ by a group $B$''
...h element $a \in A$ corresponds an automorphism $\alpha_a \in \mathrm{Aut}(B)$, which is [[conjugation]] by the element $a$:
2 KB (359 words) - 16:54, 23 November 2023
...\,b\,\omega$ or $(a,b)\omega$, but more commonly in infix form as $a \star b$ where $\star$ is the operator symbol. Many arithmetic, algebraic and logi
A binary operation is ''partial'' if it is not defined on all pairs $(a,b) \in A \times A$ (as for example division by zero is not defined). Propert
1 KB (193 words) - 19:47, 13 November 2016
...er product]] of vectors (where the product $(a,b)$ of two vectors $a$ and $b$ is, in general, a complex number) that satisfies the following axioms:
1) $(a,b)=\overline{(b,a)}$;
1 KB (173 words) - 05:40, 20 April 2023
...ddition of numbers is commutative: $a+b=b+a$, and associative: $(a+b)+c=a+(b+c)$. The operation inverse to addition is called subtraction.
739 bytes (126 words) - 20:47, 16 March 2014
Two subextensions $A$ and $B$ of an extension $\def\O{\Omega}\O$ of $k$ are called linearly disjoint if
subalgebra generated by $A$ and $B$ in $\O$ is (isomorphic to) the
1 KB (259 words) - 22:07, 5 March 2012
...out remainder. In other words, a divisor of the integer $a$ is an integer $b$ such that, for a certain integer $c$, the equality $a=bc$ holds. A ''prop
A divisor of a polynomial $A(x)$ is a polynomial $B(x)$ that divides $A(x)$ without remainder (cf. [[Division|Division]]).
1 KB (209 words) - 08:06, 26 November 2023