Counting is the mathematical action of repeatedly adding (or subtracting) one, usually to find out how many objects there are or to set aside a desired number of objects (starting with one for the first object and proceeding with an injective function from the remaining objects to the natural numbers starting from two), or for well-ordered objects, to find the ordinal number of a particular object, or to find the object with a particular ordinal number. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, a well-order relation (or well-ordering) on a set S is a Total order on S with the property that every In Set theory, an ordinal number, or just ordinal, is the Order type of a Well-ordered set. Counting is also used (primarily by children) to demonstrate knowledge of the number names and the number system. In Linguistics, a number name, or numeral, is a symbol or group of symbols or a Word in a Natural language that represents a Number A number is an Abstract object, tokens of which are Symbols used in Counting and measuring. In mathematics the term counting or enumeration also means finding the number of elements of a finite set. In Mathematics and theoretical Computer science, the broadest and most abstract definition of an enumeration of a set is an exact listing of all of its )
Counting sometimes involves numbers other than one; for example, when counting money, counting out change, when "counting by twos" (2, 4, 6, 8, 10, 12…) or when "counting by fives" (5, 10, 15, 20, 25…).
There is archeological evidence suggesting that humans have been counting for at least 50,000 years[1]. Counting was primarily used by ancient cultures to keep track of economic data such as debts and capital (i. e. , accountancy). Accountancy or accounting is the measurement statement or provision of assurance about financial information primarily used by Lenders managers, The development of counting led to the development of mathematical notation and numeral systems. See also Table of mathematical symbols Mathematical notation is used in Mathematics, and throughout the Physical sciences, Engineering A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner
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Forms
Counting can occur in a variety of forms.
Counting can be verbal; that is, speaking every number out loud (or mentally) to keep track of progress. This is often used to count objects that are present already, instead of counting a variety of things over time.
Counting can also be in the form of tally marks, making a mark for each number and then counting all of the marks when done tallying. Tally marks are an implementation of the Unary numeral system. This is useful when counting objects over time, such as the number of times something occurs during the course of a day.
Counting can also be in the form of finger counting, especially when counting small numbers. Finger counting, or dactylonomy, is the art of Counting along one's Fingers Though marginalized in modern societies by the Arabic numeral system This is often used by children to facilitate counting and simple mathematical operations. The most naive finger-counting uses unary notation (one finger = one unit) , and is thus limited to counting 10. Other hand-gesture systems are also in use, for example the Chinese system by which one can count 10 using only gestures of one hand. By using finger binary (base 2 place-value notation), it is possible to keep a finger count up to 1023 = 210 - 1. Finger binary is a system for counting and displaying binary numbers on the Fingers and Thumbs of one or more Hands It is possible
Various devices can also be used to facilitate counting, such as hand tally counters and abacuses.
Inclusive counting
Inclusive counting is usually encountered when counting days in a calendar. Normally when counting 8 days from Sunday, Monday will be day 1, Tuesday day 2, and the following Monday will be the eighth day. 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 word for fortnight is quinze jours (15 days), and similar words are present in Greek (δεκαπενθήμερο) and Spanish (quincena). This practice appears in other calendars as well; in the Roman calendar the nones (meaning nine) is 8 days before the ides; and in the Christian calendar Quinquagesima (meaning 50) is 49 days before Easter Sunday. Quinquagesima is the name for the Sunday before Ash Wednesday.
The Jewish people also counted inclusively. For instance, Jesus announced he would die and resurrect "on the third day," i. Jesus of Nazareth (7–2 BC / BCE —26–36 AD / CE) e. two days later. Scholars most commonly place his crucifixion on a Friday afternoon and his resurrection on Sunday before sunrise, spanning three different days but a period of around 36-40 hours.
Musical terminology also uses inclusive counting of interval between notes of the standard scale: going up one note is a second interval, going up two notes is a third interval, etc. In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical , and going up seven notes is an octave.
Psychology
By age 3, most children acquire the ability to count, and the majority of 3 year olds can count up to 10 objects correctly[2]. Children eventually come to understand the following 5 counting principles[2]:
- One-to-one correspondence: Each object must be labeled by a single number word.
- Stable order: The number should always be recited in the same order.
- Cardinality: The number of objects in the set is equal to the last number stated.
- Order irrelevance: Objects can be counted left to right, right to left, or in any order.
- Abstraction: Any set of discrete objects can be counted.
See also
References
- ^ An Introduction to the History of Mathematics (6th Edition) by Howard Eves (1990)p. Finger counting, or dactylonomy, is the art of Counting along one's Fingers Though marginalized in modern societies by the Arabic numeral system This article describes cardinal numbers in mathematics For cardinals in linguistics see Names of numbers in English. Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects The level of Measurement of a Variable in Mathematics and Statistics is a classification that is used to describe the nature of information Subitizing, coined in 1949 by EL Kaufman et al refers to the rapid accurate and confident judgments of Number performed for small numbers of items Tally marks are an implementation of the Unary numeral system. The unary numeral system is the bijective base - 1 Numeral system. Elementary arithmetic is the most basic kind of Mathematics: it concerns the operations of Addition, Subtraction, Multiplication, and division The area of study known as the history of mathematics is primarily an investigation into the origin of new discoveries in Mathematics and to a lesser extent an investigation Jetons were Token or Coin -like medals produced across Europe from the 13th through the 17th centuries In Set theory, an ordinal number, or just ordinal, is the Order type of a Well-ordered set. Howard Whitley Eves ( 10 January 1911 New Jersey – 6 June 2004) was an American mathematician known for his work in Geometry 9
- ^ a b Siegler, Robert (2006). How Childred Develop, Exploring Child Develop Student Media Tool Kit & Scientific American Reader to Accompany How Children Develop. New York: Worth Publishers. ISBN 0716761130.
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