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Self-descriptive Number
In mathematics, a self-descriptive number is an integer ''m'' in a given base ''b'' that is ''b'' digits long, and each digit ''d'' at position ''n'' (the most significant digit being at position 0 and the least significant at position ''b''−1) counts how many instances of digit ''n'' are in ''m''. Example For example, in base 10, the number 6210001000 is self-descriptive because of the following reasons: In base 10, the number has 10 digits, indicating its base; It contains 6 at position 0, indicating that there are six 0s in 6210001000; It contains 2 at position 1, indicating that there are two 1s in 6210001000; It contains 1 at position 2, indicating that there is one 2 in 6210001000; It contains 0 at position 3, indicating that there is no 3 in 6210001000; It contains 0 at position 4, indicating that there is no 4 in 6210001000; It contains 0 at position 5, indicating that there is no 5 in 6210001000; It contains 1 at position 6, indicating that there is one 6 in 62100010 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base. For base ten, the subscript is usually assumed and omitted (together with the enclosing parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems Generally, in a system with radix ''b'' (), a string of digits denotes the number , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Digit
A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originates from the Latin ''digiti'' meaning fingers. For any numeral system with an integer base, the number of different digits required is the absolute value of the base. For example, decimal (base 10) requires ten digits (0 to 9), and binary (base 2) requires only two digits (0 and 1). Bases greater than 10 require more than 10 digits, for instance hexadecimal (base 16) requires 16 digits (usually 0 to 9 and A to F). Overview In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, and summing the results. Di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
100 (number)
100 or one hundred (Roman numerals, Roman numeral: C) is the natural number following 99 (number), 99 and preceding 101 (number), 101. In mathematics 100 is the square of 10 (number), 10 (in scientific notation it is written as 102). The standard SI prefix for a hundred is "Hecto-, hecto-". 100 is the basis of percentages ( meaning "by the hundred" in Latin), with 100% being a full amount. 100 is a Harshad number in decimal, and also in base-four, a base in-which it is also a self-descriptive number. 100 is the sum of the first nine prime numbers, from 2 through 23 (number), 23. It is also divisible by the number of primes below it, 25 (number), 25. 100 cannot be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. 100 has a Carmichael function, reduced totient of 20, and an Euler totient of 40. A totient value of 100 is obtained from four numbers: 101 (number), 101, 125 (number), 125, 202 (number), 202, and 250 (number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
136 (number)
136 (one hundred [and] thirty-six) is the natural number following 135 (number), 135 and preceding 137 (number), 137. In mathematics 136 is: * a refactorable number and a composite number. * the 16th triangular number. * a repdigit in base 16 (88). External links 136 cats(video) References {{DEFAULTSORT:136 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipsis
The ellipsis (, plural ellipses; from , , ), rendered , alternatively described as suspension points/dots, points/periods of ellipsis, or ellipsis points, or colloquially, dot-dot-dot,. According to Toner it is difficult to establish when the "dot dot dot" phrase was first used. There is an early instance, which is perhaps the first in a piece of fiction, in Virginia Woolf's short story "An Unwritten Novel" (1920). is a punctuation mark consisting of a series of three dots. An ellipsis can be used in many ways, such as for intentional omission of text or numbers, to imply a concept without using words. Style guides differ on how to render an ellipsis in printed material. Style Opinions differ on how to render an ellipsis in printed material and are to some extent based on the technology used for rendering. According to '' The Chicago Manual of Style'', it should consist of three periods, each separated from its neighbor by a non-breaking space: . According to the '' AP ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harshad Number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Because being a Harshad number is determined based on the base the number is expressed in, a number can be a Harshad number many times over. So-called Trans-Harshad numbers are Harshad numbers in every base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit ' (joy) + ' (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. Definition Stated mathematically, let be a positive integer with digits when written in base , and let the digits be a_i (i = 0, 1, \ldots, m-1). (It follows that a_i must be either zero or a positive integer up to .) can be expressed as :X=\sum_^ a_i n^i. is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
