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- ...thesis]] or the [[Axiom of Choice]]. It is a good example of a [[diagonal argument]], a method pioneered by the mathematician [[Georg Cantor]].4 KB (757 words) - 10:44, 8 March 2018
- ...<math>BC</math>. Describe the [[locus]] of the [[intersection]]s of the [[diagonal]]s of all possible rectangles <math>DEFG</math>. ...ath>I</math> of the diagonals of <math>DEFG</math> is also the midpoint of diagonal <math>DF</math>, so2 KB (416 words) - 19:00, 21 September 2014
- ...h> on <math>\ell_r</math>, i.e. <math>a_{r\sigma(j)}=0</math>, by the same argument we have <math>s(c_\sigma(j))\ge s(c_\sigma(r))</math>, hence <math>s(\ell_j If the main diagonal contains all zeroes, we can immediately deduce from the condition that the6 KB (1,192 words) - 13:14, 29 January 2021
- ...licity). It follows that <math>y_{n}</math> is a linear combination of the diagonal elements of <math>D</math>, namely <math>r_1^n, r_2^n, \ldots, r_k^n</math> A note about this argument: all of the power series used here are defined formally, and so we do not a19 KB (3,412 words) - 13:57, 21 September 2022
- Let three-in-a-row/column/diagonal be a "win" and let player <math>0</math> be the one that fills in <math>0</ If player X takes a diagonal, player Y cannot win. If either takes a row, all the columns are blocked, a6 KB (1,057 words) - 00:58, 8 January 2023
- It is clear, that two such line segments may only intersect when they are diagonal and perpendicular to each other. But the prince has only one diagonal move at his disposal.1 KB (242 words) - 14:46, 9 January 2017
- ...ons is equal to 10<math>w</math>:6<math>w</math> = 10:6. Through a similar argument, the areas between each set of vertical lines also maintains a ratio of 10: Motivation : Notice that a cross section of any diagonal plane not going through the top or bottom face of the cylinder is an ellips11 KB (1,849 words) - 16:34, 2 December 2024
- The diagram is certainly not to scale, but the argument is sound (I believe) and involves re-ordering the construction as specified ...ts <math>BD, CE, AB</math> and <math>AC</math> and the parallelism of its diagonal and the base of the triangle formed by the perpendiculars from one vertex o4 KB (792 words) - 00:44, 19 November 2023
- * in any diagonal, if the number of entries on the diagonal is a multiple of three, then one third of the entries are <math>I</math>, o ...ells <math>(i,j)</math> for which <math>i+j</math> is a constant, and the diagonal of this second type consists all cells <math>(i,j)</math> for which <math>i3 KB (573 words) - 13:37, 4 December 2024
- ...th>. Solving we get <math>PA = 4</math>, <math>PC = 14</math>, giving us a diagonal of length <math>\sqrt{212}</math> and area <math>\boxed{106}</math>. Denote by <math>\theta</math> the argument of point <math>P</math> on the circle.22 KB (3,480 words) - 18:33, 1 August 2024
- We think about which letter is in the diagonal with <math>20</math> of a letter. We find that it is <math>2(2 + 5 + 8 + 11 ...t{P}</math> diagonal of length <math>3</math> and an <math>\text{R}</math> diagonal of length <math>1.</math>13 KB (1,839 words) - 23:54, 2 November 2024
- ...n. So, there are <math>13 - 1 = 12</math> ways to seat him. With a similar argument, the third man can be seated in <math>10</math> ways, the fourth man in <ma ...ls, and choosing <math>5</math> where there will be a single man. For each diagonal, the man can go on either side, and there are <math>\binom{14}{5}</math> wa11 KB (1,803 words) - 10:57, 30 October 2024
- This triangles lies in parallel planes, which are normal to cube diagonal <math>AC'.</math> Find the maximum value <math>F_m = max (F(x))</math> and all argument values <math>x_0</math> such that <math>F_m = F(x_0)</math>.48 KB (8,214 words) - 07:59, 30 July 2024