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  • ...2 were invited to participate in AIME. Since 2020, the AIME floor has been set to a higher percentage of scores, likely to ensure that a consistent number ...math> 10 <math>+</math> your AMC 10/12 score is equal to your USAMO/USAJMO index score.
    17 KB (1,904 words) - 18:26, 20 January 2025
  • ...select the team members during the state tournament based on [[AMC | USAMO index]], performance in local tournaments, and score at the state tournament. It ...] (Maine Association of Math Leagues) Meets. Training includes the problem set "Pete's Fabulous 42."
    22 KB (3,532 words) - 10:25, 27 September 2024
  • A zero in the index, like in <math>M_0^+</math>, tells us that <math>0</math> is also included. For a set <math>M</math>, <math>|M|=\# M</math> denotes the number of elements of <ma
    8 KB (1,401 words) - 16:49, 10 January 2025
  • ...tance in [[combinatorics]]. Let <math>I</math> be any [[nonempty]] index [[set]]. Informally, a free group on <math>I</math> is the collection of [[finit If <math>u, v</math> are elements of the free group over a set <math>I</math> and <math>uv = vu</math>, then <math>u^m = v^n</math>, for s
    2 KB (454 words) - 16:54, 16 March 2012
  • ...c_{a+1}+c_{a+2}...+c_{b-1}+c_{b}</math>. Here <math>i</math> refers to the index of summation, <math>a</math> is the lower bound, and <math>b</math> is the
    3 KB (482 words) - 15:39, 8 October 2023
  • In a [[field]] <math>F</math>, the only ideals are the set <math>\{0\}</math> and <math>F</math> itself. ...A</math> is a ring and <math>x</math> is an element of <math>A</math>, the set <math>Ax</math> is a left ideal of <math>A</math>. Ideals of this form are
    8 KB (1,389 words) - 22:44, 17 February 2020
  • ...th> and <math>P(b_j) = a_j</math> for all indices <math>j</math>. Let the set <math>\{ a_1, \dotsc, a_k, b_1, \dotsc, b_k \}</math> have <math>m</math> d ...In this case, we claim that <math>a_j + b_j</math> is constant for every index <math>j</math>. Indeed, we note that
    3 KB (704 words) - 13:42, 7 September 2021
  • ...ure that is as general as possible&mdash;a magma generated from an initial set with no constraints or relations. The free magma generated from a [[set]] <math>X</math> is constructed as follows.
    5 KB (889 words) - 17:34, 28 September 2024
  • ...ath>-coset is a union of <math>K</math>-cosets, and the cardinality of the set of <math>K</math>-cosets contained in an <math>H</math>-coset is independen so the index and order of <math>H</math> are [[divisor]]s of <math>g</math>.
    2 KB (304 words) - 11:02, 24 November 2024
  • ...oup acting on a finite set <math>S</math>; let <math>S^G</math> denote the set of fixed points of <math>S</math>. Then ''Proof.'' Let <math>G</math> act on itself by conjugation. Then the set of fixed points is the center <math>Z</math> of <math>G</math>; thus
    4 KB (814 words) - 21:50, 3 November 2023
  • ...need to trace the recurrence backwards. We only take the <math>0</math>th index for simplicity). It follows that <math>y_{n}</math> is a linear combination ..._1x} + a_2e^{r_2x} + \cdots + a_ne^{r_nx}</math>. Similarly, if there is a set of roots with multiplicity greater than <math>1</math>, say <math>r_1, r_2,
    19 KB (3,412 words) - 13:57, 21 September 2022
  • Therefore, we need only verify inequalities with an index difference of to prove the inequalities for successive even index and successive
    11 KB (1,889 words) - 12:45, 4 July 2013
  • A permutation of the set of positive integers <math>[n] = \{1, 2, \ldots, n\}</math> is a sequence < ...t necessarily distinct) for which <math>x_i + x_j < 2n</math>, there is an index <math>k</math> such that <math>x_i + x_j = x_k</math>.
    3 KB (538 words) - 12:55, 16 June 2020
  • be the set of positive integers from <math>1</math> to <math>n</math>. Let <math>M \s Let <math>P_n</math> be the set of of permutations of <math>N</math>.
    4 KB (705 words) - 21:37, 18 June 2020
  • This would return 5, which is the last element in the list. An index of -1 starts from the back of the list and gives you that element, so <code ...verything from the first number's index (inclusive) to the second number's index (but not including this number). In other words, this returns everything fr
    28 KB (4,762 words) - 20:20, 12 June 2023
  • ...,</math> because 2, 3, and 5 are all factors of 30. Therefore, since every index congruent to <math>n</math> must contain a number congruent to <math>k,</ma ...n 1 and 30 inclusive, it thus uniquely determines what number goes in each index. Furthermore, two different indices cannot contain the same number. We will
    12 KB (2,005 words) - 04:21, 24 November 2024
  • ...ts''' in [[Python]] are used to store multiple objects in a single ordered set. Unlike [[tuple]]s, lists are mutable, so entries can be added, removed, o To access the i'th element of a list, use the list name followed by the index in square brackets.
    3 KB (470 words) - 11:27, 9 September 2021
  • In [[Python]], '''sequence''' is the generic term for an ordered set. There are several types of sequences in Python, the following three are t ...n are '''zero-indexed''', so the first element has index 0, the second has index 1, and so on.
    3 KB (426 words) - 18:39, 7 December 2024
  • ...ples''' in [[Python]] are used to store multiple items in a single ordered set. However, unlike [[list]]s, tuples are ''immutable'' - they can't be chang ...ess the i'th element of a tuple, use the name of the tuple followed by the index in square brackets. Note that like other [[sequence (Python)|sequences]] i
    1 KB (196 words) - 16:18, 19 April 2011
  • ...eet is full of water. A solid cube with side length <math>8</math> feet is set into the barrel so that the diagonal of the cube is vertical. The volume of ...n \sin{k}</math>, where <math>k</math> represents radian measure. Find the index of the 100th term for which <math>a_n < 0</math>.
    8 KB (1,326 words) - 18:15, 13 January 2024

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