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119 (number)
119 (one hundred [and] nineteen) is the natural number following 118 (number), 118 and preceding 120 (number), 120. Mathematics * 119 is a Perrin number, preceded in the sequence by 51, 68, 90 (it is the sum of the first two mentioned). * 119 is the sum of five consecutive Prime number, primes (17 + 19 + 23 + 29 + 31). * 119 is the sum of seven consecutive Prime number, primes (7 + 11 + 13 + 17 + 19 + 23 + 29). * 119 is a highly cototient number. * 119 is one of five numbers to hold a Divisor function, sum-of-divisors of 144 (number), 144 = 12 (number), 122 (the others are 66 (number), 66, 70 (number), 70, 94 (number), 94, and 115 (number), 115). * 119 is the Order (group theory), order of the largest Cyclic group, cyclic subgroups of the monster group. * 119 is the smallest composite number that is 1 less than a factorial (120 is 5!). * 119 is a semiprime, and the fourth in the family. Telephony * 119 (emergency telephone number), 119 is an emergency telephone number in some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
115 (number)
115 (one hundred [and] fifteen) is the natural number following 114 (number), 114 and preceding 116 (number), 116. In mathematics 115 has a square number, square sum of divisors: :\sigma(115)=1+5+23+115=144=12^2. There are 115 different rooted trees with exactly eight nodes, 115 inequivalent ways of placing six Rook (chess), rooks on a 6 × 6 chess board in such a way that no two of the rooks attack each other, and 115 solutions to the Map folding, stamp folding problem for a strip of seven stamps. 115 is also a heptagonal pyramidal number. The 115th Woodall number, :115\cdot 2^-1=4\;776\;913\;109\;852\;041\;418\;248\;056\;622\;882\;488\;319, is a prime number. 115 is the sum of the first five heptagonal numbers. See also * 115 (other) References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
119 (emergency Telephone Number)
119 (one-one-nine) is an emergency telephone number in parts of Asia and in Jamaica. From May 2020, 119 was introduced in the United Kingdom as the single non-emergency number for the COVID-19 testing helpline in England, Wales, and Northern Ireland. From January 2022, 119 was introduced in Romania as the single non-emergency number for reporting cases of abuse, neglect, exploitation and any other form of violence against the child. Afghanistan The 119 Information Center of the Minister of Interior Affairs was founded in 2009 in Kabul city with 58 employees operating 24 hours a day. This main goal of this information center is to give citizens an opportunity to report complaints of police misbehavior, corruption, and human rights violations, criminal and terrorist activity. In 2013, with the help of the public, the 119 information prevented many dangerous attacks against people and property. In 2020, the national police disabled 173 mines, discovered 15 suicide vests, and arr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k- almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime number, prime, or the Unit (ring theory), unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monster Group
In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has order : : = 2463205976112133171923293141475971 : ≈ . The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families or is one of 26 sporadic groups that do not follow such a systematic pattern. The monster group contains 20 sporadic groups (including itself) as subquotients. Robert Griess, who proved the existence of the monster in 1982, has called those 20 groups the ''happy family'', and the remaining six exceptions '' pariahs''. It is difficult to give a good constructive definition of the monster because of its complexity. Martin Gardner wrote a popular account of the monster group in his June 1980 Mathematical Games column in ''Scientific American''. History The monster was predi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgroups
In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G. Formally, given a group under a binary operation ∗, a subset of is called a subgroup of if also forms a group under the operation ∗. More precisely, is a subgroup of if the restriction of ∗ to is a group operation on . This is often denoted , read as " is a subgroup of ". The trivial subgroup of any group is the subgroup consisting of just the identity element. A proper subgroup of a group is a subgroup which is a proper subset of (that is, ). This is often represented notationally by , read as " is a proper subgroup of ". Some authors also exclude the trivial group from being proper (that is, ). If is a subgroup of , then is sometimes called an overgroup of . The same definitions apply more generally when is an arbitrary semigroup, but this article will only deal with subgroups ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Group
In abstract algebra, a cyclic group or monogenous group is a Group (mathematics), group, denoted C_n (also frequently \Z_n or Z_n, not to be confused with the commutative ring of P-adic number, -adic numbers), that is Generating set of a group, generated by a single element. That is, it is a set (mathematics), set of Inverse element, invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. Each element can be written as an integer Exponentiation, power of g in multiplicative notation, or as an integer multiple of g in additive notation. This element g is called a ''Generating set of a group, generator'' of the group. Every infinite cyclic group is isomorphic to the additive group \Z, the integers. Every finite cyclic group of Order (group theory), order n is isomorphic to the additive group of Quotient group, Z/''n''Z, the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order (group Theory)
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is ''infinite''. The ''order'' of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element of a group, is thus the smallest positive integer such that , where denotes the identity element of the group, and denotes the product of copies of . If no such exists, the order of is infinite. The order of a group is denoted by or , and the order of an element is denoted by or , instead of \operatorname(\langle a\rangle), where the brackets denote the generated group. Lagrange's theorem states that for any subgroup of a finite group , the order of the subgroup divides the order of the group; that is, is a divisor of . In particular, the order of any element is a divisor of . Example The symmetric group S3 ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
94 (number)
94 (ninety-four) is the natural number following 93 and preceding 95. In mathematics 94 is: *the twenty-ninth distinct semiprime and the fourteenth of the form (2.q). *the ninth composite number in the 43-aliquot tree. The aliquot sum of 94 is 50 within the aliquot sequence; (94, 50, 43, 1,0). *the second number in the third triplet of three consecutive distinct semiprimes, 93, 94 and 95 *a 17- gonal number and a nontotient. *an Erdős–Woods number, since it is possible to find sequences of 94 consecutive integers such that each inner member shares a factor with either the first or the last member. *a Smith number in decimal. In computing The ASCII character set (and, more generally, ISO 646) contains exactly 94 graphic non- whitespace characters, which form a contiguous range of code points. These codes ( 0x21–0x7E, as corresponding high bit set bytes 0xA1–0xFE) also used in various multi-byte encoding schemes for languages of East Asia, such as ISO 2022, EUC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
118 (number)
118 (one hundred [and] eighteen) is the natural number following 117 (number), 117 and preceding 119 (number), 119. In mathematics There is no answer to the equation Euler's totient function, φ(''x'') = 118, making 118 a nontotient. Four expressions for 118 as the sum of three positive integers have the same product: :14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118 and :14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800. 118 is the smallest number that can be expressed as four sums with the same product in this way. Because of its expression as , it is a Leyland number#Leyland_number_of_the_second_kind, Leyland number of the second kind. 118!! - 1 is a prime number, where !! denotes the double factorial (the product of even integers up to 118). See also * 118 (other) References [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
