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- ...ath>|N| > |K|</math> (as in our problem) is that there exists a surjective mapping from <math>N</math> to <math>K</math>, but not an injection. In other words11 KB (1,986 words) - 18:13, 19 June 2024
- ...ath> and translate it to attach side <math>AB</math> onto <math>AC</math>, mapping <math>\triangle ABC</math> to <math>\triangle CAD</math>. Point <math>P</ma9 KB (1,505 words) - 22:17, 31 December 2024
- ...alternative example, if we take the function <math>f(x) = \frac1x</math>, mapping to the real numbers, our domain could be the set of all reals except zero,1 KB (228 words) - 22:17, 16 August 2013
- Let <math>a</math> be an element of <math>R</math>. Then the mapping <math>x \mapsto ax</math> of <math>R</math> into <math>R</math> is an [[end Let <math>\mathcal{F}</math> be the set of weak [[multiplicative function]]s mapping the positive [[integer]]s into themselves. Then the elements of <math>\mat6 KB (994 words) - 05:16, 8 April 2015
- ...<math>S^S</math> be the set of [[function]]s on <math>S</math>. We call a mapping <math>a \mapsto f_a</math> from <math>M</math> to <math>S^S</math> a ''left We say that a monoid's action on <math>S</math> is ''faithful'' if the mapping <math>a\mapsto f_a</math> is [[injective]], i.e., for any distinct <math>a,3 KB (670 words) - 21:45, 21 May 2008
- ...th> and <math>CC_0</math> are concurrent at point <math>G</math> and <i><b>Mapping theorem</b></i>. <i><b>Mapping theorem</b></i>59 KB (10,203 words) - 03:47, 30 August 2023
- ...rk: A permutation <math>f </math> of a set <math>S </math> is a one-to-one mapping of <math>S </math> onto itself. An element <math>i </math> in <math>S </ma3 KB (604 words) - 17:54, 10 May 2023
- ...rk: A permutation <math>f </math> of a set <math>S </math> is a one-to-one mapping of <math>S </math> onto itself. An element <math>i </math> in <math>S </ma3 KB (459 words) - 13:24, 17 September 2023
- ...thety is <math>\frac{AD}{AB}</math>, which is also the scale factor of the mapping of the intersection of diagonals (the original we call <math>X</math> and t2 KB (416 words) - 19:00, 21 September 2014
- ...or the vector space <math> \displaystyle A </math> of continuous functions mapping some interval <math> I \mapsto \mathbb{R} </math>, the operator <math> \dis2 KB (356 words) - 15:46, 15 April 2007
- ...perp EF, OE \perp ED </math>, it follows that there is a spiral similarity mapping <math> \displaystyle AOE </math> to <math> \displaystyle FDE </math>, i.e., ...> \displaystyle E </math> with rotation of <math> {} \frac{\pi}{2} </math> mapping triangle <math> \displaystyle AOE </math> to triangle <math> \displaystyle10 KB (1,539 words) - 22:37, 6 June 2007
- for any functions <math>a,b </math> mapping subsets of <math> \mathbb{N} </math> into <math> \mathbb{C} </math>. In pa3 KB (613 words) - 20:40, 21 June 2009
- continuous [[partial derivative]]s mapping an open set containing2 KB (381 words) - 11:12, 30 May 2019
- ...ordered set]]s, a homomorphism from <math>A</math> to <math>B</math> is a mapping <math>\phi : A \to B</math> such that for all <math>a, b \in A</math>, if < ...aw of <math>*</math>, then a homomorphism <math>\phi : A \to B</math> is a mapping such that for all <math>a,b \in A</math>,2 KB (303 words) - 14:33, 11 February 2024
- ...the same object. Isomorphic objects cannot be distinguished by universal mapping properties.600 bytes (86 words) - 20:13, 2 September 2008
- ...Indeed, if <math>G</math> is a group, then for <math>a \in G</math>, the mapping <math>x \mapsto ax</math> is a permutation of <math>G</math>. Thus symmetr ...''' if it contains an even number of inversions. We wish to show that the mapping <math>\sigma \mapsto (-1)^{\nu(\sigma)}</math> is a [[homomorphism]]; this10 KB (1,668 words) - 14:33, 25 May 2008
- .../math> centered at the origin. It now suffices to find what happens to the mapping of the region <math>R-R_2</math> (in blue below).6 KB (894 words) - 17:56, 25 December 2022
- '''Corollary 4.''' The mapping <math>f: \rm G' \mapsto G'/N</math> is a bijection from the set of subgroup15 KB (2,840 words) - 11:22, 9 April 2019
- ...G</math>. This mapping is denoted <math>\text{Int}(a)</math>. Every such mapping is an automorphism. ...nt}(a)</math> is a group automorphism on <math>G</math>. Furthermore, the mapping <math>\text{Int}:a \mapsto \text{Int}(a)</math> is a group homomorphism fro3 KB (481 words) - 20:07, 14 May 2008
- ...lpha a + \beta b, \alpha a - \beta b)</math> is an automorphism, as is the mapping <math>(a,b) \mapsto (b,a)</math>. Thus if <math>(a,0)</math> (<math>a \neq4 KB (701 words) - 22:30, 14 May 2008