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- ...satisfy. These axioms are chosen to agree with our intuitive concept of a set, on one hand, and to allow various, sometimes quite sophisticated, mathemat ...t are called the [[element]]s of the set. A common misconception is that a set can have multiple indistinct elements, such as the following: <math>\{1,4,511 KB (2,021 words) - 00:00, 17 July 2011
- Let <math> S </math> be the set of [[ordered pair]]s <math> (x, y) </math> such that <math> 0 < x \le 1, 0<y\le 1, </mat2 KB (303 words) - 22:28, 11 September 2020
- ...<math> m </math> consecutive integers whose sum is <math> 2m, </math> and set <math> B </math> consists of <math> 2m </math> consecutive integers whose s ...are on adjacent sides of the square. The midpoints of the line segments in set <math> S </math> enclose a region whose area to the nearest hundredth is <m9 KB (1,434 words) - 13:34, 29 December 2021
- The function <math>f</math>, defined on the set of ordered pairs of positive integers, satisfies the following properties:6 KB (902 words) - 08:57, 19 June 2021
- How many ordered four-tuples of integers <math>(a,b,c,d)\,</math> with <math>0 < a < b < c < .../math>, are then drawn randomly and without replacement from the remaining set of <math>997</math> numbers. Let <math>p</math> be the probability that, af8 KB (1,275 words) - 06:55, 2 September 2021
- For certain ordered pairs <math>(a,b)\,</math> of real numbers, the system of equations ...lution is an ordered pair <math>(x,y)\,</math> of integers. How many such ordered pairs <math>(a,b)\,</math> are there?7 KB (1,141 words) - 07:37, 7 September 2018
- Find the number of [[ordered pair]]s <math>(x,y)</math> of positive integers that satisfy <math>x \le 2y Let <math>n</math> be the number of ordered quadruples <math>(x_1,x_2,x_3,x_4)</math> of positive odd [[integer]]s that7 KB (1,084 words) - 02:01, 28 November 2023
- There is a set of 1000 switches, each of which has four positions, called <math>A, B, C</m Let <math>\mathcal{T}</math> be the set of ordered triples <math>(x,y,z)</math> of nonnegative real numbers that lie in the pl7 KB (1,094 words) - 13:39, 16 August 2020
- For how many ordered pairs <math>(x,y)</math> of integers is it true that <math>0 < x < y < 10^{ ...ays and at <math>14</math> miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within six minutes. The area7 KB (1,204 words) - 03:40, 4 January 2023
- ...e digits of Dick's age. Let <math>d</math> be Dick's present age. How many ordered pairs of positive integers <math>(d,n)</math> are possible? ...ct squares in the plane of the dodecagon have at least two vertices in the set <math>\{A_1,A_2,A_3,\ldots,A_{12}\}</math>?8 KB (1,374 words) - 21:09, 27 July 2023
- For simplicity purposes, we set <math>c=\frac14,</math> which gives <cmath>Q(k)=-\frac13Q(k-1).</cmath> Thus, our desired number of paths is equivalent to the number of ordered septuples of positive integers <math>(b_1, b_2, \ldots, b_7)</math> such th17 KB (2,837 words) - 13:34, 4 April 2024
- ...a</math> in the range <math>0<k<1000</math>, or <math>49\cdot12=588</math> ordered pairs <math>(a,b)</math>. If <math>a=0</math>, <math>b\neq0</math>, which includes <math>11</math> ordered pairs.12 KB (1,859 words) - 18:16, 28 March 2022
- The function <math>f</math>, defined on the set of ordered pairs of positive integers, satisfies the following properties:4 KB (538 words) - 13:24, 12 October 2021
- .../math>, are then drawn randomly and without replacement from the remaining set of <math>997</math> numbers. Let <math>p</math> be the probability that, af There is a total of <math>P(1000,6)</math> possible ordered <math>6</math>-tuples <math>(a_1,a_2,a_3,b_1,b_2,b_3).</math>5 KB (772 words) - 09:04, 7 January 2022
- ...deck has 27 cards, with every shape-color-shade combination represented. A set of three cards from the deck is called complementary if all of the followin ...\binom{27}{2} = 27*13 = 351</math> possibilities. Note, however, that each set is generated by <math>{3\choose 2} = 3</math> pairs, so we've overcounted b3 KB (585 words) - 19:37, 25 April 2022
- ...for any <math>i</math> and <math>j</math>. Let <math>D_{40}</math> be the set of all dominos whose coordinates are no larger than 40. Find the length of We can draw a comparison between the domino a set of 40 points (labeled 1 through 40) in which every point is connected with9 KB (1,671 words) - 22:10, 15 March 2024
- If <math>\{a_1,a_2,a_3,\ldots,a_n\}</math> is a [[set]] of [[real numbers]], indexed so that <math>a_1 < a_2 < a_3 < \cdots < a_n ...all possible subsets of <math>\{1,2,\ldots,8\}</math>. Since the sets are ordered, a <math>9</math> must go at the end; hence we can just append a <math>9</m2 KB (384 words) - 19:02, 20 October 2023
- Let <math>n</math> be the number of ordered quadruples <math>(x_1,x_2,x_3,x_4)</math> of positive odd [[integer]]s that ...however note that the quadruples all need to be odd. This motivates us to set <math>x_i= 2y_i +1</math>, as for all integers <math>y_i</math>, <math>2y_i5 KB (684 words) - 11:41, 13 August 2023
- Let <math>\mathcal{T}</math> be the set of ordered triples <math>(x,y,z)</math> of nonnegative [[real number]]s that lie in th3 KB (445 words) - 19:40, 4 July 2013
- Call the number <math>\overline{abcd}</math>. Then <math>a+b=c+d</math>. Set <math>a+b=x</math>. ...\leq k \leq 18</math>, we notice that there are <math>(18 - k) + 1</math> ordered pairs with a sum of <math>k</math>.4 KB (696 words) - 11:55, 10 September 2023
