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  • ...ence of <math>\sf{AC}</math>, one can define cardinals using [[equivalence classes]], formed via the relation <math>X\sim Y\Leftrightarrow|X|=|Y|</math> (ther
    2 KB (263 words) - 23:54, 16 November 2019
  • ...f [[equivalence class]]es of <math>R</math> under the relation of provable equivalence. Let <math>\hat 0</math> denote the set of statements which are provably f
    4 KB (717 words) - 19:01, 25 April 2009
  • ...each other. Thus the relation partitions <math>S_{k-1} </math> into two [[equivalence class]]es; we pick the larger one, which must have at least <math>2^{n-k} +
    2 KB (392 words) - 13:34, 7 March 2010
  • A '''quotient set''' is a [[set]] derived from another by an [[equivalence relation]]. ...and let <math>\mathcal{R}</math> be an equivalence relation. The set of [[equivalence class]]es of <math>S</math> with respect to <math>\mathcal{R}</math> is cal
    2 KB (358 words) - 08:42, 7 June 2016
  • ...The relations <math>x^{-1}y \in H</math>, <math>xy^{-1} \in H</math> are [[equivalence relation]]s. ''Proof.'' We prove that the first relation is an equivalence relation; the second then follows by passing to the opposite law on <math>G
    4 KB (897 words) - 00:28, 3 September 2008
  • ...<math>\text{Frac}(R)</math> as the set of [[equivalence class|equivalence classes]] of <math>S</math> under <math>\sim</math>.
    2 KB (439 words) - 13:09, 4 March 2022
  • ...let <math>\pi_1(X,x_0)=\Omega(X,x_0)/\sim</math> be the set of equivalence classes of <math>\Omega(X,x_0)</math> under <math>\sim</math>. ...h> and <math>Y</math> satisfy the weaker notion of equivalence: [[homotopy equivalence]].
    8 KB (1,518 words) - 19:11, 23 January 2017
  • ...bspace of <math>X</math> containing <math>x,y</math>, then the resulting [[equivalence class]]es are called the '''components''' of <math>X</math>. In a sense, th The '''quasicomponents''' are the equivalence classes resulting from the equivalence relation <math>x \sim y</math> if there does not exist a separation <math>X
    3 KB (497 words) - 15:27, 15 March 2010
  • ...the relation <math>R = \{(j, k)\in [n]\times[n]\mid jk\in S\}</math> is an equivalence relation on <math>[n]</math>. ...> into its equivalence class. Suppose there are <math>N</math> equivalence classes: <math>C_1, \ldots, C_N</math>. Let <math>n_i</math> be the number of eleme
    12 KB (2,336 words) - 14:28, 28 October 2024