Difference between revisions of "Number"
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| − | + | '''Number''' is an abstraction of the concept of quantity. The earliest number systems consisted solely of [[natural numbers]]; however, as needs arose, these were expanded to more complex concepts, such as [[decimals]]. | |
Numbers are usually represented in [[English]] writing by a system of ''numerals'': | Numbers are usually represented in [[English]] writing by a system of ''numerals'': | ||
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*9 (nine) | *9 (nine) | ||
| − | + | which can be used in combination to approximate any real number to arbitrary precision. An older system of representation, still sometime encountered on clocks and other places, is [[Roman numeral]]s, which used certain letters of the [[alphabet]] instead. | |
There are many kinds of numbers. Some examples are: | There are many kinds of numbers. Some examples are: | ||
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*[[Complex number]]s | *[[Complex number]]s | ||
*[[Transcendental number]]s | *[[Transcendental number]]s | ||
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| + | It should be noted that number systems further removed from the natural numbers frequently have counter-intuitive properties. For instance, the complex numbers are ''not'' an [[ordered field]], and cannot be represented on a single line. Other even more abstruse constructions are the [[quaternions]] and the [[octonions]]; whilst these are both sometimes called number systems, whether these deserve to be called so is another matter. Essentially, the concept of number is not amenable to definition. | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 17:08, November 14, 2009
Number is an abstraction of the concept of quantity. The earliest number systems consisted solely of natural numbers; however, as needs arose, these were expanded to more complex concepts, such as decimals.
Numbers are usually represented in English writing by a system of numerals:
- 0 (zero)
- 1 (one)
- 2 (two)
- 3 (three)
- 4 (four)
- 5 (five)
- 6 (six)
- 7 (seven)
- 8 (eight)
- 9 (nine)
which can be used in combination to approximate any real number to arbitrary precision. An older system of representation, still sometime encountered on clocks and other places, is Roman numerals, which used certain letters of the alphabet instead.
There are many kinds of numbers. Some examples are:
- Prime numbers
- Composite numbers
- Rational numbers
- Real numbers
- Imaginary numbers
- Complex numbers
- Transcendental numbers
It should be noted that number systems further removed from the natural numbers frequently have counter-intuitive properties. For instance, the complex numbers are not an ordered field, and cannot be represented on a single line. Other even more abstruse constructions are the quaternions and the octonions; whilst these are both sometimes called number systems, whether these deserve to be called so is another matter. Essentially, the concept of number is not amenable to definition.
