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34-415: 1,000,000 ( one million ), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione ( milione in modern Italian), from mille , "thousand", plus the augmentative suffix -one . It is commonly abbreviated: In scientific notation , it is written as 1 × 10 or 10. Physical quantities can also be expressed using

68-427: A totient value of 1000 (1111, 1255, ..., 3750). One thousand is also equal to the sum of Euler's totient summatory function Φ ( n ) {\displaystyle \Phi (n)} over the first 57 integers. In decimal , multiples of one thousand are totient values of four-digit repdigits : In the list of composite numbers , 7777 is very nearly the composite index of 8888: 8886

102-448: A (finite) set, the answer is the same. In a broader context, the theorem is an example of a theorem in the mathematical field of (finite) combinatorics —hence (finite) combinatorics is sometimes referred to as "the mathematics of counting." Many sets that arise in mathematics do not allow a bijection to be established with {1, 2, ..., n } for any natural number n ; these are called infinite sets , while those sets for which such

136-465: A bijection does exist (for some n ) are called finite sets . Infinite sets cannot be counted in the usual sense; for one thing, the mathematical theorems which underlie this usual sense for finite sets are false for infinite sets. Furthermore, different definitions of the concepts in terms of which these theorems are stated, while equivalent for finite sets, are inequivalent in the context of infinite sets. The notion of counting may be extended to them in

170-642: A bijection with the natural numbers, and these sets are called " uncountable ." Sets for which there exists a bijection between them are said to have the same cardinality , and in the most general sense counting a set can be taken to mean determining its cardinality. Beyond the cardinalities given by each of the natural numbers, there is an infinite hierarchy of infinite cardinalities, although only very few such cardinalities occur in ordinary mathematics (that is, outside set theory that explicitly studies possible cardinalities). Counting, mostly of finite sets, has various applications in mathematics. One important principle

204-419: A bijection with the original set is not excluded. For instance, the set of all integers (including negative numbers) can be brought into bijection with the set of natural numbers, and even seemingly much larger sets like that of all finite sequences of rational numbers are still (only) countably infinite. Nevertheless, there are sets, such as the set of real numbers , that can be shown to be "too large" to admit

238-404: A million years" and "You're one in a million", or a hyperbole , as in "I've walked a million miles" and "You've asked a million-dollar question". 1,000,000 is also the square of 1000 and also the cube of 100 . Even though it is often stressed that counting to precisely a million would be an exceedingly tedious task due to the time and concentration required, there are many ways to bring

272-489: A year after learning these skills for a child to understand what they mean and why the procedures are performed. In the meantime, children learn how to name cardinalities that they can subitize . In mathematics, the essence of counting a set and finding a result n , is that it establishes a one-to-one correspondence (or bijection) of the subject set with the subset of positive integers {1, 2, ..., n }. A fundamental fact, which can be proved by mathematical induction ,

306-531: Is 7919 . It is a difference of 1 from the order of the smallest sporadic group : | M 11 | = 7920 {\displaystyle |\mathrm {M} _{11}|=7920} . There are 135 prime numbers between 1000 and 2000: Counting#Counting in mathematics Counting sometimes involves numbers other than one; for example, when counting money, counting out change, "counting by twos" (2, 4, 6, 8, 10, 12, ...), or "counting by fives" (5, 10, 15, 20, 25, ...). There

340-602: Is a third interval, etc., and going up seven notes is an octave . Learning to count is an important educational/developmental milestone in most cultures of the world. Learning to count is a child's very first step into mathematics, and constitutes the most fundamental idea of that discipline. However, some cultures in Amazonia and the Australian Outback do not count, and their languages do not have number words. Many children at just 2 years of age have some skill in reciting

374-460: Is also the 16th generalized 30-gonal number. 1000 is the Wiener index of cycle length 20 , also the sum of labeled boxes arranged as a pyramid with base 1 – 20. 1000 is the element of multiplicity in a 24 × 24 {\displaystyle 24\times 24} toroidal board in the n -Queens problem , with respective indicator of 25 and count of 51 . 1000

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408-511: Is archaeological evidence suggesting that humans have been counting for at least 50,000 years. Counting was primarily used by ancient cultures to keep track of social and economic data such as the number of group members, prey animals, property, or debts (that is, accountancy ). Notched bones were also found in the Border Caves in South Africa, which may suggest that the concept of counting

442-496: Is sometimes known, from Ancient Greek , as a chiliad . A period of one thousand years may be known as a chiliad or, more often from Latin , as a millennium . The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand . It is the first 4-digit integer . 1000 is the 10th icositetragonal number, or 24-gonal number. It

476-407: Is still useful for some things. Refer also to the fencepost error , which is a type of off-by-one error . Modern mathematical English language usage has introduced another difficulty, however. Because an exclusive counting is generally tacitly assumed, the term "inclusive" is generally used in reference to a set which is actually counted exclusively. For example; How many numbers are included in

510-452: Is that if two sets X and Y have the same finite number of elements, and a function f : X → Y is known to be injective , then it is also surjective , and vice versa. A related fact is known as the pigeonhole principle , which states that if two sets X and Y have finite numbers of elements n and m with n > m , then any map f : X → Y is not injective (so there exist two distinct elements of X that f sends to

544-419: Is that no bijection can exist between {1, 2, ..., n } and {1, 2, ..., m } unless n = m ; this fact (together with the fact that two bijections can be composed to give another bijection) ensures that counting the same set in different ways can never result in different numbers (unless an error is made). This is the fundamental mathematical theorem that gives counting its purpose; however you count

578-457: Is the 7779th composite number. Also, 1600 = 40 is the totient value of 4000, as well as 6000, whose collective sum is 10000, where 6000 is the totient of 9999, one less than 10 . The sum of the first nine prime numbers up to 23 is 100, with φ ( p ( 23 ) ) = 1000 {\displaystyle \varphi (p(23))=1000} , where p ( 23 ) = 1255 {\displaystyle p(23)=1255}

612-473: Is the number of integer partitions of 23. Using decimal representation as well, On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973 . 1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers: all represent prime numbers. Adding the prime 853 with its prime index of 147 yields 1000. The one-thousandth prime number

646-443: Is the number of strict partitions of 50 containing the sum of no subset of the parts . A chiliagon is a 1000-sided polygon , of order 2000 in its regular form . 1000 has a reduced totient value λ ( n ) {\displaystyle \lambda (n)} of 100 , and Euler totient φ ( n ) {\displaystyle \varphi (n)} of 400 . 11 integers have

680-501: The SI prefix mega (M), when dealing with SI units; for example, 1 megawatt (1 MW) equals 1,000,000 watts . The meaning of the word "million" is common to the short scale and long scale numbering systems, unlike the larger numbers, which have different names in the two systems. The million is sometimes used in the English language as a metaphor for a very large number, as in "Not in

714-764: The ides ; more generally, dates are specified as inclusively counted days up to the next named day. In the Christian liturgical calendar , Quinquagesima (meaning 50) is 49 days before Easter Sunday. When counting "inclusively", the Sunday (the start day) will be day 1 and therefore the following Sunday will be the eighth day . For example, the French phrase for " fortnight " is quinzaine (15 [days]), and similar words are present in Greek (δεκαπενθήμερο, dekapenthímero ), Spanish ( quincena ) and Portuguese ( quinzena ). In contrast,

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748-427: The English word "fortnight" itself derives from "a fourteen-night", as the archaic " sennight " does from "a seven-night"; the English words are not examples of inclusive counting. In exclusive counting languages such as English, when counting eight days "from Sunday", Monday will be day 1 , Tuesday day 2 , and the following Monday will be the eighth day . For many years it was a standard practice in English law for

782-438: The count list (that is, saying "one, two, three, ..."). They can also answer questions of ordinality for small numbers, for example, "What comes after three ?". They can even be skilled at pointing to each object in a set and reciting the words one after another. This leads many parents and educators to the conclusion that the child knows how to use counting to determine the size of a set. Research suggests that it takes about

816-499: The difference in usage between the terms "inclusive counting" and "inclusive" or "inclusively", and one must recognize that it's not uncommon for the former term to be loosely used for the latter process. Inclusive counting is usually encountered when dealing with time in Roman calendars and the Romance languages . In the ancient Roman calendar , the nones (meaning "nine") is 8 days before

850-431: The end of each interval. For inclusive counting, unit intervals are counted beginning with the start of the first interval and ending with end of the last interval. This results in a count which is always greater by one when using inclusive counting, as compared to using exclusive counting, for the same set. Apparently, the introduction of the number zero to the number line resolved this difficulty; however, inclusive counting

884-401: The following prime counts: In total, there are 586,081 prime numbers between 1,000,000 and 10,000,000. 1000 (number) 1000 or one thousand is the natural number following 999 and preceding 1001 . In most English-speaking countries , it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000 . A group of one thousand things

918-579: The four fingers and the three bones in each finger ( phalanges ) to count to twelve. Other hand-gesture systems are also in use, for example the Chinese system by which one can count to 10 using only gestures of one hand. With finger binary it is possible to keep a finger count up to 1023 = 2 − 1 . Various devices can also be used to facilitate counting, such as tally counters and abacuses . Inclusive/exclusive counting are two different methods of counting. For exclusive counting, unit intervals are counted at

952-454: The number "down to size" in approximate quantities, ignoring irregularities or packing effects. In Indian English and Pakistani English , it is also expressed as 10 lakh . Lakh is derived from lakṣa for 100,000 in Sanskrit . There are 78,498 primes less than 10, where 999,983 is the largest prime number smaller than 1,000,000. Increments of 10 from 1 million through a 10 million have

986-480: The phrase "from a date" to mean "beginning on the day after that date": this practice is now deprecated because of the high risk of misunderstanding. Similar counting is involved in East Asian age reckoning , in which newborns are considered to be 1 at birth. Musical terminology also uses inclusive counting of intervals between notes of the standard scale: going up one note is a second interval, going up two notes

1020-441: The same element of Y ); this follows from the former principle, since if f were injective, then so would its restriction to a strict subset S of X with m elements, which restriction would then be surjective, contradicting the fact that for x in X outside S , f ( x ) cannot be in the image of the restriction. Similar counting arguments can prove the existence of certain objects without explicitly providing an example. In

1054-404: The sense of establishing (the existence of) a bijection with some well-understood set. For instance, if a set can be brought into bijection with the set of all natural numbers, then it is called " countably infinite ." This kind of counting differs in a fundamental way from counting of finite sets, in that adding new elements to a set does not necessarily increase its size, because the possibility of

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1088-426: The set that ranges from 3 to 8, inclusive? The set is counted exclusively, once the range of the set has been made certain by the use of the word "inclusive". The answer is 6; that is 8-3+1, where the +1 range adjustment makes the adjusted exclusive count numerically equivalent to an inclusive count, even though the range of the inclusive count does not include the number eight unit interval. So, it's necessary to discern

1122-511: Was known to humans as far back as 44,000 BCE. The development of counting led to the development of mathematical notation , numeral systems , and writing . Verbal counting involves speaking sequential numbers aloud or mentally to track progress. Generally such counting is done with base 10 numbers: "1, 2, 3, 4", etc. Verbal counting is often used for objects that are currently present rather than for counting things over time, since following an interruption counting must resume from where it

1156-490: Was left off, a number that has to be recorded or remembered. Counting a small set of objects, especially over time, can be accomplished efficiently with tally marks : making a mark for each number and then counting all of the marks when done tallying. Tallying is base 1 counting. Finger counting is convenient and common for small numbers. Children count on fingers to facilitate tallying and for performing simple mathematical operations. Older finger counting methods used

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