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• Infinity
  ...e a [[infinite]] number of digits because they never end. The first use of infinity was during Ancient Greek by Anaximander who referred to it as "apeiron". Th
  454 bytes (71 words) - 01:38, 6 July 2018

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• Inequality
  ...on]]. Closed bounds use square brackets, while open bounds (and bounds at infinity) use parentheses. For instance, <math>x \in [3,6)</math> means <math>3 \le
  12 KB (1,806 words) - 06:07, 19 June 2024
• Number theory/Advanced
  ...ion to consider the point infinitely far vertically upward as the point at infinity. We denote it by <math>\mathcal{O}</math>. ...effort showing that this defines a group, but it can be done. The point at infinity <math>\mathcal{O}</math> is the identity for this group, and an inverse is
  5 KB (849 words) - 16:14, 18 May 2021
• Harmonic series
  This sum slowly approaches infinity.
  2 KB (334 words) - 20:52, 13 March 2022
• Goldbach Conjecture
  Since this quantity goes to infinity as <math>n</math> increases, we expect that every large even integer has no
  7 KB (1,201 words) - 16:59, 19 February 2024
• Infinite
  ==Applications to Infinity with Sums== A sum works the same way. Certain sums equate to infinity, such as
  1 KB (186 words) - 23:19, 16 August 2013
• 1989 AIME Problems/Problem 10
  ...on equals <math>\tan^2 \alpha</math> as <math>\tan \beta</math> approaches infinity.
  8 KB (1,401 words) - 21:41, 20 January 2024
• Interval
  Use latex \infty for infinity symbol and use latex \cup for OR symbol.
  1 KB (219 words) - 19:34, 5 January 2024
• 2006 Romanian NMO Problems
  ...ht\rfloor \right)_{n \geq 0}</math> are an infinity of even numbers and an infinity of odd numbers.
  11 KB (1,779 words) - 14:57, 7 May 2012
• Euler line
  ...frac{y_B}{x_E}= \frac {y_F}{x_A}</math> then point <math>I</math> moves to infinity and lines are parallel, angles <math>\angle APD = 60^\circ</math> or <math>
  59 KB (10,203 words) - 04:47, 30 August 2023
• 2003 AMC 12A Problems/Problem 25
  ...ys has a vertex, and always extends until <math>+</math> or <math>-</math> infinity, depending on the <math>a</math> value. Quite conveniently, we have an <mat
  9 KB (1,606 words) - 11:34, 10 July 2020
• Asymptote (geometry)
  ...Since the denominator increases faster than the numerator, as x approaches infinity, y gets smaller until it approaches zero. A similar trend can be seen as x
  4 KB (664 words) - 11:44, 8 May 2020
• 2007 AIME II Problems/Problem 14
  ...y large, and the limit of <math>g(x)</math> as <math>|x|</math> approaches infinity is 1, so <math>g(x)</math>=1 for all x, or <math>f(x)=f(-x)</math>. Then <
  7 KB (1,335 words) - 17:44, 25 January 2022
• 2004 IMO Shortlist Problems/G2
  Again, we use projective geometry. We send <math> \ell </math> to infinity, so that <math> \displaystyle \Gamma </math> becomes an ellpise with axis < .../math> are parallel, i.e., they pass through the same point on the line at infinity as <math> \displaystyle GA </math>, i.e., <math> \displaystyle F </math>.
  10 KB (1,539 words) - 23:37, 6 June 2007
• Zermelo-Fraenkel Axioms
  === The Axiom of Infinity ===
  4 KB (732 words) - 20:49, 13 October 2019
• Aleph null
  '''Aleph null''' (<math>\aleph_{0}</math>) is the [[infinity|infinite]] quantity with the least magnitude. It generally is regarded as a
  847 bytes (120 words) - 20:49, 26 October 2007
• 1997 USAMO Problems/Problem 2
  ...h>DEF</math>. Clearly, these lines are parallel and concur at the point of infinity.
  2 KB (347 words) - 08:13, 26 August 2021
• L'Hôpital's Rule
  Note that the points surrounding <math>z(a)</math> aren't approaching infinity, as a function like <math>f(x) = 1/x-1</math> might at <math>f(a)</math>.
  2 KB (475 words) - 15:04, 24 March 2022
• Isogonal conjugate
  ...sformation of the plane that maps the point <math>O</math> into a point at infinity and the line <math>\ell</math> maps to itself. In this case, the isogonals The preimage of <math>Z'</math> is located at infinity on the line <math>l.</math>
  54 KB (9,416 words) - 08:40, 18 April 2024
• Momentum
  ...ange in momentum) needed to increase the speed further would also approach infinity.
  2 KB (271 words) - 09:02, 11 March 2008
• 2008 AIME I Problems/Problem 12
  ...ss and less significant, so we take the limit as <math>n</math> approaches infinity
  4 KB (669 words) - 18:35, 8 October 2023

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