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• Sequence
  ...e''' is an ordered list of terms. Sequences may be either [[finite]] or [[infinite]]. ...uch that for all integers <math>n \ge k</math>, we have <math>|x_n - L| < \epsilon</math>. If <math>(x_n)</math> converges to <math>L</math>, <math>L</math>
  2 KB (413 words) - 20:18, 13 November 2022
• Riemann zeta function
  expressed as an infinite product: \lim_{\epsilon \to 0} \epsilon \phi(1+\epsilon)
  9 KB (1,547 words) - 02:04, 13 January 2021
• Analysis
  ...of mathematical analysis was set by Bolzano when he introduced the modern epsilon delta definition of continuity and Cauchy who tried to put calculus on a "f ...unctions. More generally, functional analysis studies what are essentially infinite dimensional vector spaces and its generalizations.
  2 KB (352 words) - 17:12, 8 February 2015
• Symmetric group
  ...at in general this theorem is not true on infinite sets without permitting infinite compositions of functions. ...</math> to the multiplicative group <math>\{-1,1\}</math> such that <math>\epsilon(\tau) = -1</math>, for any transposition <math>\tau</math>.
  10 KB (1,668 words) - 14:33, 25 May 2008
• 0.999...
  ...</math>, there exists an integer <math>N>0</math> such that <math>|a_n-L|<\epsilon</math> for all integers greater than <math>N</math>. So in fact, we had to === Infinite series ===
  3 KB (577 words) - 19:04, 4 February 2023
• Proofs without words
  The infinite [[geometric series]] <math>\frac 12 + \frac {1}{2^2} + \frac {1}{2^3} + \cd The infinite [[geometric series]] <math>\frac 13 + \frac {1}{3^2} + \frac {1}{3^3} + \cd
  55 KB (7,998 words) - 15:07, 16 September 2024
• Bolzano-Weierstrass Theorem
  ...rvals, and label the rightmost interval <math>I_2</math>. Since there are infinite points in <math>I_2</math> we can pick some <math>a_{n_2}\in I_2</math>, an ...</math> are contained in each interval, it follows that <math>|a_{n_k}-x|<\epsilon</math>.
  1 KB (270 words) - 16:18, 12 June 2022
• Searching the community
  ...posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". | Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)
  21 KB (3,334 words) - 22:53, 23 March 2022