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  • ...in some larger [[partially ordered set]] <math>R</math>, a '''least upper bound''' or '''supremum''', for <math>S</math> is an [[element]] <math>M \in R</m If the least upper bound <math>M</math> of <math>S</math> is an element of <math>S</math>, it is als
    1,011 bytes (177 words) - 13:08, 5 March 2022
  • ...some larger [[partially ordered set]] <math>R</math>, a '''greatest lower bound''' or '''infimum''' for <math>S</math> is an [[element]] <math>m \in R</mat If the greatest lower bound <math>m</math> of <math>S</math> is an element of <math>S</math>, it is als
    597 bytes (109 words) - 12:55, 5 March 2022

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  • The set of Real numbers is a [[Least upper bound|complete]], [[Order relation|ordered]] [[field]] under addition and multipl Let <math>M\in\mathbb{R}</math> be an [[bounded|upper bound]] of <math>A</math>
    3 KB (496 words) - 22:22, 5 January 2022
  • ...rship] is offering a $1,000 scholarship opportunity to college and college-bound students who have suffered a serious injury.
    7 KB (1,039 words) - 17:45, 18 January 2024
  • ...ower of <math>a</math> then <math>\lceil \log_a(m)\rceil</math> is a lower bound on <math>c</math>.
    4 KB (680 words) - 11:54, 16 October 2023
  • ...{\sqrt n}</math> grows slower than any geometric progression, so the upper bound can be replaced by <math>\gamma^n</math> with any <math>\gamma\in(4\Gamma,
    8 KB (1,431 words) - 12:48, 26 January 2008
  • This lower bound can be achieved if we use <math>b_1 = -1</math>, <math>b_2 = 0</math>, <mat
    8 KB (1,332 words) - 13:39, 8 December 2024
  • Apply Cauchy's inequality to bound the sum, yielding <math>(1+1)\left((a+b+c+d)^{2}+(e+f+g+h)^{2}\right) \ge (
    3 KB (584 words) - 00:17, 17 July 2024
  • Let <math>M</math> be an upper bound for <math>\lvert f(x) \rvert</math>. Now, let <math>N(R)</math> be an upper bound for the quantity
    6 KB (1,034 words) - 06:55, 12 August 2019
  • ...of the product as a quadratic, then <math>((x-1)^2+\sqrt{2006})</math> is bound to hold the two non-real roots since the other definitely crosses the x-ax
    4 KB (686 words) - 11:52, 13 June 2024
  • The bound on <math>a</math> is easier to handle with , so lets start putting values o
    11 KB (1,857 words) - 11:57, 18 July 2024
  • ...e book, where the upper bound maximizes the sum of the pages and the lower bound maximizes the extra page (and thus minimizes the total sum of the pages.) ...+ 1)}{2} = 1986</math> is the quadratic you must solve to obtain the upper bound of <math>n</math> and <math>\frac{n(n + 1)}{2} + n = 1986</math>
    2 KB (336 words) - 13:13, 6 September 2020
  • ...elves appear on at most <math>n-1</math> dominos each. This gives an upper bound of dominos in the longest proper sequence in <math>D_{n}.</math> This bound is in fact attained for every even <math>n.</math> It is easy to verify thi
    9 KB (1,659 words) - 17:35, 20 June 2024
  • This line and the x and y axis bound the region the truck can go if it moves in the positive x direction. Simila
    4 KB (642 words) - 17:25, 28 November 2024
  • ...ath> is a perfect square, but the only perfect squares that are within our bound on <math>a-b</math> are <math>1</math> and <math>4</math>. We know <math>a+
    5 KB (845 words) - 18:23, 17 September 2023
  • with the bound determined by the factor with the largest value of
    9 KB (1,699 words) - 12:48, 11 April 2020
  • its radius of convergence is the greatest lower bound of the distance upper bound on <math>\lvert f(z) \rvert</math> for <math>z\in C</math>. By the
    9 KB (1,537 words) - 20:04, 26 July 2017
  • ...phrase "maximum value" in the original problem is changed to "least upper bound of", then the problem should have the solution above.
    3 KB (541 words) - 16:32, 22 November 2023
  • ...massless gluons, but since they are confined, all we see are color-neutral bound states of gluons, called glueballs. All the glueballs are massive, which is
    2 KB (363 words) - 14:31, 1 December 2015
  • The volume of an object defined by an upper bound of <math>f(x,y,z)</math> in the Cartesian three-space can be found using a
    3 KB (523 words) - 19:24, 17 August 2023
  • ...f positive integers ordered by the [[divisor]] [[relation]], [[least upper bound]]s exist for any finite set.)
    692 bytes (106 words) - 10:15, 19 April 2008
  • #REDIRECT[[Least upper bound]]
    30 bytes (4 words) - 19:21, 3 November 2006

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