"Fairy tern The fairy tern (""Sternula nereis"") is a small tern which is native to the southwestern Pacific. It is listed as ""Vulnerable"" by the IUCN and the New Zealand subspecies is ""Critically Endangered"". There are three subspecies: The fairy tern is a small tern with a white body and light bluish-grey wings. The crown and nape is black. It can be distinguished from the little tern in that a black band extends no further than the eye and not as far as the bill. In the breeding plumage both the beak and the legs are yellowish-orange. During the rest"
"ten using the cardinal numbers for 'two' to 'five' with the plural of 'ten'. 'Sixty' to 'one hundred' are numerical nouns in their own right, derived from the same roots as the nouns for 'six' to 'ten' but with different class prefixes. In a similar pattern, 'two hundred' to 'five hundred' are expressed as multiples of a hundred using the cardinal numbers with the plural of 'hundred'. Then 'six hundred' to 'one thousand' are nouns, again derived from the same roots as 'six' to 'ten'. The pattern repeats up to 'ten thousand', then standard nouns are used for 'ten thousand',"
"Triple system In algebra, a triple system (or ternar) is a vector space ""V"" over a field F together with a F-trilinear map The most important examples are Lie triple systems and Jordan triple systems. They were introduced by Nathan Jacobson in 1949 to study subspaces of associative algebras closed under triple commutators anticommutator]]s {""u"", {""v"", ""w""}}. In particular, any [[Lie algebra]] defines a Lie triple system and any [[Jordan algebra]] defines a Jordan triple system. They are important in the theories of [[symmetric space]]s, particularly [[Hermitian symmetric space]]s and their generalizations ([[symmetric R-space]]s and their noncompact duals). A triple"
"""S"". The number of ""k""-combinations of an ""n""-set, ""C""(""n"",""k""), is therefore related to the number of ""k""-permutations of ""n"" by: These numbers are also known as binomial coefficients and denoted formula_68. Ordered arrangements of the elements of a set ""S"" of length ""n"" where repetition is allowed are called ""n""-tuples, but have sometimes been referred to as permutations with repetition although they are not permutations in general. They are also called words over the alphabet ""S"" in some contexts. If the set ""S"" has ""k"" elements, the number of ""n""-tuples over ""S"" is: There is no restriction on how often"
"Ternary operation In mathematics, a ternary operation is an ""n""-ary operation with ""n"" = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A. An example of a ternary operation is the product in a heap. In computer science, a ternary operator is an operator that takes three arguments. The arguments and result can be of different types. Many programming languages that use C-like syntax feature a ternary operator, codice_1, which defines a conditional expression. Since this operator is often the only existing ternary operator"
"and 4, were the distributive numerals: , , , , , , and so on. The meaning of these is 'one each', 'two each' (or 'in pairs') and so on, for example ""ibī turrīs cum ternīs tabulātīs ērigēbat"" 'there he began erecting towers with three storeys each' (Julius Caesar); ""bīnī senātōrēs singulīs cohortibus praepositī"" 'a pair of senators was put in charge of each group of soldiers' (Livy). In numbers 13 to 19, the order may be inverted, e.g. ""dēnī ternī"" instead of ""ternī dēnī"". The word ""singulī"" is always plural in this sense in the classical period: From the"
"than the problems with the extensions of tetration, there are several open questions concerning tetration, particularly when concerning the relations between number systems such as integers and irrational numbers Tetration In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, but before pentation and is as such defined as iterated exponentiation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration. Tetration is used for the notation of very large numbers. The notation formula_1 means formula_2, which is the application of exponentiation formula_3 times. The first four hyperoperations are shown here, with tetration being the fourth"
"to the number of (""k"" − 1)-element subsets of a set with ""n"" − 1 elements. Both of these numbers are given by the binomial coefficient formula_1. For example, when ""n"" = 3 and ""k"" = 2, the tuples counted by the theorem are (2, 1) and (1, 2), and there are formula_2 of them. For any pair of positive integers ""n"" and ""k"", the number of ""k""-tuples of non-negative integers whose sum is ""n"" is equal to the number of multisets of cardinality ""k"" − 1 taken from a set of size ""n"" + 1. Both numbers are given"
"of the number is written in ternary form. Ternary numbers can be used to convey self–similar structures like the Sierpinski triangle or the Cantor set conveniently. Additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have a ternary expression that does not contain any instance of the digit 1. Any terminating expansion in the ternary system is equivalent to the expression that is identical up to the term preceding"
"expressions to mean 1 or more. For example, 913 means the set An example are the following eight sequences: In each case, every term is divisible by one of the primes . These primes can be said to form a covering set exactly analogous to Sierpinski and Riesel numbers. The covering set is found for several similar sequences, including: An even simpler case can be found in the sequence: Here, it can be shown that if: Thus we have a covering set with only three primes {3, 7, 13}. This is only possible because the sequence gives integer terms ""only"
"Tetration In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, but before pentation and is as such defined as iterated exponentiation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration. Tetration is used for the notation of very large numbers. The notation formula_1 means formula_2, which is the application of exponentiation formula_3 times. The first four hyperoperations are shown here, with tetration being the fourth of these (in this case, the unary operation succession, formula_4, is considered to be the zeroth operation). Here, succession is the most basic operation; addition () is a primary"
"noun serving as a direct object is unmarked, and so are citation forms. In an equational clause with an implicit ""be"" verb, both nouns are left unmarked (the accusative form). Like other Surmic languages, Tennet uses a modified vigesimal counting system. ""Six"" is derived from ""five and one,"" ""seven"" from ""five and two,"" etc. ""Ten"" is a new word, followed by ""ten and one,"" ""ten and two,"" up to ""ten and five and four,"" after which is a new word for ""twenty,"" which means ""a person"" (10 fingers and 10 toes). ""Forty"" is ""two people,"" sixty is ""three people,"" etc."
"Set (mathematics) In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. The concept of a set is one of the most fundamental in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary"
"Sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called ""elements"", or ""terms""). The number of elements (possibly infinite) is called the ""length"" of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and order matters. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first ""n"" natural numbers (for a sequence of finite length ""n""). The position of"
"by the multiset number formula_3, or equivalently by the binomial coefficient formula_4 or multiset number formula_5. For example, when ""n"" = 3 and ""k"" = 2, the tuples counted by the theorem are (3, 0), (2, 1), (1, 2), and (0, 3), and there are formula_6 of them. Suppose one has ""n"" objects (to be represented as stars; in the example below ""n"" = 7) to be placed into ""k"" bins (in the example ""k"" = 3), such that all bins contain at least one object; one distinguishes the bins (say they are numbered 1 to ""k"") but one does"
"Ternary numeral system The ternary numeral system (also called base 3) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log 3 (about 1.58496) bits of information. Although ""ternary"" most often refers to a system in which the three digits are all non–negative numbers, specifically , , and , the adjective also lends its name to the balanced ternary system, comprising the digits −1, 0 and +1, used in comparison logic and ternary computers. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly"
"(~149 tags) uses six: ""NN2 - plural common noun, NNL2 - plural locative noun, NNO2 - numeral noun, plural, NNT2 - temporal noun, plural, NNU2 - plural unit of measurement, NP2 - plural proper noun."" Plural The plural (sometimes abbreviated ), in many languages, is one of the values of the grammatical category of number. Plural of nouns typically denote a quantity other than the default quantity represented by a noun, which is generally one (the form that represents this default quantity is said to be of ""singular"" number). Most commonly, therefore, plurals are used to denote two or more"
"display much less variety. The inherited cardinal numeral system consists of ten numerals (still in active use) and three numeral nouns (now obsolete) for ""a tensome"", ""a hundred"" and ""a thousand"". There is also an indefinite numeral meaning ""several, many"" or ""how many?"" which morphologically and syntactically patterns with the numerals 1 to 10. For numbers of 20 and over, Arabic numerals are commonly used. These are listed below. The formation of feminine ""one"" and ""two"" is irregular. The numerals 1 to 10 are constructed with nouns (inflected nouns in the EA), the gender of the numeral agreeing with that"
"lists of length . -tuples whose entries come from a set of elements are also called ""arrangements with repetition"", ""permutations of a multiset"" and, in some non-English literature, ""variations with repetition"". The number of -tuples of an -set is . This follows from the combinatorial rule of product. If is a finite set of cardinality , this number is the cardinality of the -fold Cartesian power . Tuples are elements of this product set. In type theory, commonly used in programming languages, a tuple has a product type; this fixes not only the length, but also the underlying types of"
"defined here. The term ""ternary ring"" often means a planar ternary ring, but it can also simply mean a ternary system. A planar ternary ring is a structure formula_1 where formula_2 is a set containing at least two distinct elements, called 0 and 1, and formula_6 is a mapping which satisfies these five axioms: When formula_2 is finite, the third and fifth axioms are equivalent in the presence of the fourth. No other pair (0', 1') in formula_19 can be found such that formula_20 still satisfies the first two axioms. Define formula_21. The structure formula_22 is a loop with identity"
"""tapuisga'q"" for 20, ""nesisga'q"" for 30, etc.) While 10, 20, 30, 40 and 50 all use a single word containing a prefix, the tens between 60 and 90 use the numeral as a preceding word to a separate word meaning ten, ""te'sisga'q"": for instance, 60 is written as ""as'gom te'sisga'q"". Numbers between the tens are stated through multiple-word phrases, beginning with the ten-based root number, such as ""ne'wtisgaq"", followed by ""jel"" (meaning ""and"" or ""also"") and ending with one of the nine numerals: for instance, the number 28 is constructed as ""tapuisga'q jel ugumuljin"", or literally ""twenty and eight"". For"
"or three nines somewhere. This is not true for all real numbers. Heilbronn set In mathematics, a Heilbronn set is an infinite set ""S"" of natural numbers for which every real number can be arbitrarily closely approximated by a fraction whose denominator is in ""S"". For any given real number formula_1 and natural number formula_2, it is easy to find the integer formula_3 such that formula_4 is closest to formula_1. For example, for the real number formula_6 and formula_7 we have formula_8. If we call the closeness of formula_1 to formula_4 the difference between formula_11 and formula_3, the closeness is"
"Sperner's theorem Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family. It is one of the central results in extremal set theory, and is named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name ""Sperner's lemma"" also refers to an unrelated result on coloring triangulations. To differentiate the two results, the result on the size of a Sperner family is now more commonly known as Sperner's theorem. A family of sets that does not include two sets"
"in the language, it is sometimes simply referred to as """"the"" ternary operator"". In some languages, this operator is referred to as ""the conditional operator"". Another example for a ternary operator is ""between"", as used in SQL. Ternary operation In mathematics, a ternary operation is an ""n""-ary operation with ""n"" = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A. An example of a ternary operation is the product in a heap. In computer science, a ternary operator is an operator that takes three"
"trilinear forms determined by an element of These arise in particular when formula_25 above is semisimple, when the Killing form provides a duality between formula_26 and formula_27. [[Category:Representation theory]] Triple system In algebra, a triple system (or ternar) is a vector space ""V"" over a field F together with a F-trilinear map The most important examples are Lie triple systems and Jordan triple systems. They were introduced by Nathan Jacobson in 1949 to study subspaces of associative algebras closed under triple commutators anticommutator]]s {""u"", {""v"", ""w""}}. In particular, any [[Lie algebra]] defines a Lie triple system and any [[Jordan algebra]]"
"of tens, are formed by adding the word ""k'átsi"" (/ kʼátsʰɪ / 'ten') ""f""ollowed by the word ""dzidra (""/tsɪtʂa/ 'more'). Numerals 20 and above are formed by adding a multiplicative adverb (""-wa"" or ""-ya"") to the base number and the word ""k'átsi"". European colonizers arriving in the Southwest US brought with them material culture and concepts that were unknown to the peoples living in the area. Words for the new ideas introduced by Spaniards were often borrowed into Keres directly from Early Modern Spanish, and a large number of these persists in Modern Keresan. Keres was one of the seven"
"Pentation In mathematics, pentation is the next hyperoperation after tetration but before hexation. It is defined as iterated (repeated) tetration, just as tetration is iterated exponentiation. It is a binary operation defined with two numbers ""a"" and ""b"", where ""a"" is tetrated to itself ""b"" times. The word ""pentation"" was coined by Reuben Goodstein in 1947 from the roots penta- (five) and iteration. It is part of his general naming scheme for hyperoperations. There is little consensus on the notation for pentation; as such, there are many different ways to write the operation. However, some are more used than others,"
"rule is that each element is the sum of the previous two elements, and the first two elements are 0 and 1. The first ten terms of this sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, and 34. A more complicated example of a sequence that is defined recursively is Recaman's sequence. We can define Recaman's sequence by Not all sequences can be specified by a rule in the form of an equation, recursive or not, and some can be quite complicated. For example, the sequence of prime numbers is the set of prime numbers in their"
"be reversed (so that the second entry is smaller than the first, then the third larger than the second, and so on), while others call both types by the name alternating permutation. The determination of the number ""A"" of alternating permutations of the set {1, ..., ""n""} is called André's problem. The numbers ""A"" are known as Euler numbers, zigzag numbers, or up/down numbers. When ""n"" is even the number ""A"" is known as a secant number, while if ""n"" is odd it is known as a tangent number. These latter names come from the study of the generating function"
"topologies on a set with ""n"" elements. It also lists the number of inequivalent (i.e. nonhomeomorphic) topologies. Let ""T""(""n"") denote the number of distinct topologies on a set with ""n"" points. There is no known simple formula to compute ""T""(""n"") for arbitrary ""n"". The Online Encyclopedia of Integer Sequences presently lists ""T""(""n"") for ""n"" ≤ 18. The number of distinct T topologies on a set with ""n"" points, denoted ""T""(""n""), is related to ""T""(""n"") by the formula where ""S""(""n"",""k"") denotes the Stirling number of the second kind. Finite topological space In mathematics, a finite topological space is a topological space"
"noun is neither singular nor plural, but rather ambiguous as to number. This is called ""transnumeral"" or sometimes ""general number,"" abbreviated . Many such languages have optional number marking, which tends to be used for definite and highly animate referents, most notably first-person pronouns. The languages of the Tanoan family have three numbers – singular, dual, and plural – and exhibit an unusual system of marking number, called ""inverse number"" (or ""number toggling""). In this scheme, every countable noun has what might be called its ""inherent"" or ""expected"" numbers, and is unmarked for these. When a noun appears in an"
"A 1‑tuple is called a singleton, a 2‑tuple is called an ordered pair and a 3‑tuple is a triple or triplet. can be any nonnegative integer. For example, a complex number can be represented as a 2‑tuple, a quaternion can be represented as a 4‑tuple, an octonion can be represented as an 8‑tuple and a sedenion can be represented as a 16‑tuple. Although these uses treat ""‑tuple"" as the suffix, the original suffix was ""‑ple"" as in ""triple"" (three-fold) or ""decuple"" (ten‑fold). This originates from medieval Latin ""plus"" (meaning ""more"") related to Greek ‑πλοῦς, which replaced the classical and late"
"topics from set theory such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree. The German word ""Menge"", rendered as ""set"" in English, was coined by Bernard Bolzano in his work ""The Paradoxes of the Infinite"". A set is a well-defined collection of distinct objects. The objects that make up a set (also known as the set's ""elements"" or ""members"") can be anything: numbers, people, letters of the alphabet, other sets, and so on. Georg Cantor, one of the founders of set theory, gave the following definition of"