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- ...ted by a letter or symbol. Many contest problems test one's fluency with [[algebraic manipulation]]. [[algebraic number theory]] and [[analytic number theory]].6 KB (902 words) - 17:16, 22 October 2024
- ...pon a variable. However, when multiplying/dividing both sides by negative numbers, we have to flip the sign. ...h>1</math>. Therefore, these two aren't solutions. Then we begin to test numbers such as <math>2</math>, <math>3</math>, and so on. All of these work. In12 KB (1,806 words) - 05:07, 19 June 2024
- ...ization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually <math>x</math> and <math>y</math> are variables and < ...n. When their sum is subtracted from their product, which of the following numbers could be obtained?4 KB (682 words) - 12:13, 8 December 2024
- Its elementary algebraic formulation is often referred to as '''Cauchy's Inequality''' and states th ...ct vector spaces. Under this formulation, the elementary algebraic, linear algebraic, and calculus formulations are different cases of the general inequality.13 KB (2,048 words) - 14:28, 22 February 2024
- ...h a certain subset of the real numbers, such as [[integer]]s, [[positive]] numbers, [[natural number]]s, [[rational number]]s, etc. Some [[algebra]]ic topics3 KB (399 words) - 22:08, 8 January 2024
- == Algebraic Number Theory == ...<math>\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})</math>. Famous problems in algebraic number theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fe5 KB (849 words) - 15:14, 18 May 2021
- ...eal numbers are:<math>1, 2, -23.25, 0, \frac{\pi}{\phi}</math>, and so on. Numbers that are not real are <math>\ 3i</math>, <math>\ 3+2.5i</math>, <math>\ 3+ ...eans negative integers. The real numbers can also be divided between the [[algebraic number]]s and [[transcendental number]]s, although these two classes are b3 KB (496 words) - 22:22, 5 January 2022
- ===Algebraic proof=== '''Algebraic Proof'''12 KB (1,993 words) - 22:47, 27 October 2024
- ...number pi often shows up in problems in [[number theory]], particularly [[algebraic number theory]]. For example, many [[class number]] formulae involve pi. ...be read right after its parent article [[rational approximation of famous numbers]], but an unexperienced reader may prefer to read the proof that [[ln 2 is8 KB (1,469 words) - 20:11, 16 September 2022
- ..., one can say that the irrational numbers make up "almost all" of the real numbers. There are two types of irrational numbers: algebraic and transcendental.3 KB (368 words) - 18:26, 6 June 2015
- ...Liouville Approximation Theorem]] provides one way of showing that certain numbers are transcendental. * [[Algebraic number]]568 bytes (72 words) - 10:52, 9 December 2007
- ...e from the irrational number <math>x</math> to some finite set of rational numbers, i.e., less than some positive constant. ...in various ways. The first way is that one can try to approximate several numbers simultaneously by fractions with common denominator. The exact statement is7 KB (1,290 words) - 11:18, 30 May 2019
- ...[analysis]], since the result depends on certain properties of the complex numbers that are most naturally described in [[topology | topological]] terms. === Algebraic Proof ===5 KB (832 words) - 13:22, 11 January 2024
- ...ac{4+\sqrt[27]{19}}{\sqrt[3]{4}+\sqrt[7]{97}}</math>. A number that is not algebraic is called a [[transcendental number]], such as <math>e</math> or <math>\pi< ===Number of algebraic numbers===1 KB (153 words) - 11:30, 27 September 2024
- ...tions by means of [[abstract algebra]], and in particular [[ring theory]]. Algebraic geometry is most easily done over [[algebraically closed]] [[field]]s, but == Affine Algebraic Varieties ==2 KB (361 words) - 00:59, 24 January 2020
- of the prime numbers; in this same paper, he posed the * Koch, Helmut (trans. David Kramer), ''Number Theory: Algebraic Numbers and Functions'', AMS Graduate Studies in Mathematics 2000, ISBN 0-8218-205410 KB (1,729 words) - 18:52, 21 October 2023
- * Koch, Helmut (trans. David Kramer), ''Number Theory: Algebraic Numbers and Functions.'' AMS 2000, ISBN 0-8218-2054-0.9 KB (1,547 words) - 02:04, 13 January 2021
- ...iophantine equation|Diophantine equations]], testing whether certain large numbers are prime, and even some problems in cryptology. Notice that if we pick two numbers <math>a</math> and <math>b</math> from the same set, then <math>a</math> an14 KB (2,317 words) - 18:01, 29 October 2021
- ...g, but we can easily solve this problem by finding patterns, recursion and algebraic manipulations. ...^k+2^k\Longrightarrow O<2^{k-R}</math> so there are <math>2^{k-R-1}</math> numbers that satisfy this form.10 KB (1,702 words) - 21:23, 25 July 2024
- ===In algebraic form=== ...coefficients will always be an algebraic number. General formulas give the algebraic form of the roots of polynomials with degree at most <math>4</math>.8 KB (1,427 words) - 20:37, 13 March 2022