Search results

* 概率论（Probability Theory） # [[组合数学 (Fall 2019)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] （ [http://tcs.nju.edu.cn/slides/comb2019/Polya.pdf ...

The set of [[natural number]]s is '''not''' an alphabet because as it is not finite. * Michael A. Harrison, ''Introduction to Formal Language Theory'', (1978): Chapter 1.2 ...

In [[mathematics]], a '''Mersenne number''' is a number that is one less than a ''power of two''. ...the definition of a Mersenne number where exponent ''n'' has to be a prime number. ...

In [[mathematics]], a '''Ramanujan prime''' is a [[prime number]] that satisfies a result proven by [[Srinivasa Ramanujan]]. It relates to ...)'' is the [[prime counting function]]. The prime counting function is the number of primes less than or equal to ''x''. ...

...any elements are in H, called the order of H) divides |G|. Moreover, the number of distinct left (right) [[coset]]s of H in G is |G|/|H|. ...

* 概率论（Probability Theory） # [[组合数学 (Fall 2023)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] ([http://tcs.nju.edu.cn/slides/comb2023/Polya.pdf ...

...ss the test, and that are not prime. These numbers are called [[Carmichael number]]s. ...the equality does not hold for a value of ''a'', then ''n'' is [[composite number|composite]] (not prime). If the equality does hold for many values of ''a' ...

...ors are for values close to zero and [[hue]] encodes the value's [[complex number|argument]]. ...med after [[Bernhard Riemann]], who wrote about it in the memoir "[[On the Number of Primes Less Than a Given Quantity]]", published in 1859. ...

A '''Fermat number''' is a special [[positive number|positive]] [[number]]. Fermat numbers are named after [[Pierre de Fermat]]. The formula that ge ...a power of two. Every prime of the form 2^''n'' + 1 is a Fermat number, and such primes are called '''Fermat primes'''. The only known Fermat prim ...

* 概率论（Probability Theory） # [[Combinatorics (Fall 2010)/Extremal set theory|Extremal set theory]] | [http://lamda.nju.edu.cn/yinyt/notes/comb2010/comb8.pdf slides] ...

...eory]]. He proved that the answer to his problem was smaller than Graham's number. ...ers ever used in a [[mathematical proof]]. Even if every digit in Graham's number were written in the tiniest writing possible, it would still be too big to ...

* 概率论（Probability Theory） # [[组合数学 (Fall 2024)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] ([http://tcs.nju.edu.cn/slides/comb2024/Polya.pdf ...

...contributed to many areas of learning. Most of his work was about [[number theory]] and [[astronomy]]. ...her once tried to keep the children busy, telling them to add up all the [[number]]s from 1 to 100. Gauss did it quickly, like this: 1 + 100 = 101, 2 + 99 = ...

...ame way that all real numbers can be thought of as 1 multiplied by another number. Arithmetic functions such as, [[addition]], subtraction, [[multiplication] ...o pose real problems for mathematicians. As a comparison, using [[negative number]]s, it is possible to find the ''x'' in the [[equation]] <math>a + x = b</m ...

...82845904523536, come close to the true value. The true value of ''e'' is a number that never ends. Euler himself gave the first 23 digits of e.<ref>[[Leonhar ...onential function]]s. For example, the exponential function applied to the number one, has a value of ''e''. ...

...the complex plane. The real part <math>\operatorname{Re}(s)</math> of the number is drawn horizontally, the imaginary part <math>\operatorname{Im}(s)</math> ...rom Riemann's functional equation. More have been computed and have [[real number|real]] part 1/2. The hypothesis states all the undiscovered zeros must hav ...

...argument ''x'' fixed at 10. In [[number theory]], the concept of [[p-adic number]]s is also closely related to that of a power series. ...

...as there is no real number that will multiply by itself to get a negative number (e.g. 3*3 = 9 and -3*-3 = 9). ...mbers is a lot like multiplying a '''positive number''' with a '''negative number'''. If I say "go east by 2*-3 miles" it means "rotate all of the way around ...

...ction of two numbers can produce a negative number, which is not a natural number, but it is an integer. ...osure of [[intersection]]. Open sets have infinite closure of [[union (set theory)|union]]. That is, in mathematical notation, if A₀, and A<sub>1< ...

Mathematics is the study of [[number]]s, [[shape]]s and [[pattern]]s. The word is sometimes shortened to '''mat === Number === ...