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Self-descriptive Number
In mathematics, a self-descriptive number is an integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ... ''m'' that in a given base ''b'' is ''b'' digits long in which 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, indicat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. 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 natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) 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, although for base ten the subscript is usually assumed (and omitted, together with the pair of 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 In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Digit
A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ''digiti'' meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective ''decem'' meaning ten) digits. For a given numeral system with an integer base, the number of different digits required is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) requires two digits (0 and 1). 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
100 (number)
100 or one hundred (Roman numeral: C) is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to describe the long hundred of six score or 120. In mathematics 100 is the square of 10 (in scientific notation it is written as 102). The standard SI prefix for a hundred is " hecto-". 100 is the basis of percentages (''per cent'' meaning "per 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. It is also divisible by the number of primes below it, 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 reduced totient of 20, and an Euler totient of 40. A totient value of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
136 (number)
136 (one hundred ndthirty six) is the natural number following 135 and preceding 137. In mathematics 136 is itself a factor of the Eddington number. With a total of 8 divisors, 8 among them, 136 is a refactorable number. It is a composite number. 136 is a centered triangular number and a centered nonagonal number. The sum of the ninth row of Lozanić's triangle is 136. 136 is a self-descriptive number in base 4, and a repdigit in base 16. In base 10, the sum of the cubes of its digits is 1^3 + 3^3 + 6^3 = 244. The sum of the cubes of the digits of 244 is 2^3 + 4^3 + 4^3 = 136. 136 is a triangular number, because it's the sum of the first 16 positive integers. In the military * Force 136 branch of the British organization, the Special Operations Executive (SOE), in the South-East Asian Theatre of World War II * USNS ''Mission Soledad'' (T-AO-136) was a United States Navy ''Mission Buenaventura''-class fleet oiler during World War II * USS ''Admirable'' (AM-136) was a United ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipsis
The ellipsis (, also known informally as dot dot dot) is a series of dots that indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning. The plural is ellipses. The term originates from the grc, ἔλλειψις, meaning 'leave out'. Opinions differ as to how to render ellipses in printed material. 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 Stylebook'', the periods should be rendered with no space between them: . A third option is to use the Unicode character U+2026 . Background The ellipsis is also called a suspension point, points of ellipsis, periods of ellipsis, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harshad Number
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. 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 a harshad number in base if: :X \equiv 0 \bmod . A number which is a harshad number in every number base is called an all-harshad number, or an all-Niven number. There are only four all-harshad numbers: 1, 2, 4, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
