Témbongkeun sumber pikeun Wilangan

{{Orphan|date=April 2017}}

'''Wilangan''' atawa angka nyaéta hiji entitas abstrak pikeun ngagambarkeun [[quantity]]. Aya sababaraha jenis wilangan. Nu pada mikawanoh nyaéta [[angka natural]]s {0, 1, 2, ...} digunakeun pikeun [[ngawilang]] jeung dilambangkeun ku '''N'''. Upama [[angka negatip|negative]] ogé diasupkeun, mangka urang meunang [[wilangan buleud]] '''Z'''. Rasio wilangan buleud disebut [[rational angka]] atawa [[fractions]]; kumpulan sakabéh wilangan rasional dilambangkeun ku '''Q'''. Wilangan rasional bisa dituliskeun ku wilangan desimal nu ngabogaan digit nu kawates atawa periodik. Umpamana sakabéh wilangan desimal nu teu kawates jeun nu teu periodik diasupkeun, mangka dihasilkeun wilangan [[nyata(real)]] s '''R'''. Wilangan nyata anu henteu rasional disebut wilangan [[wilangan irrasional]] . Wilangan réal bisa dilegakeun ka [[wilangan kompleks]] '''C''' pikeun mecahkeun sakabéh sasaruaan aljabar. Lambang di luhur biasana ditulis ku huruf [[kandel]], nyaéta:
:<math>\mathbb{N}\sub\mathbb{Z}\sub\mathbb{Q}\sub\mathbb{R}\sub\mathbb{C}</math>

Wilangan komplek ka hareupna bisa leuwih dilegakeun [[quaternion]]s, but multiplication of quaternions is not [[commutative]]. [[Octonion]]s, in turn, extend the quaternions, but this time, [[associativity]] is lost. In fact, the only finite-dimensional associative [[division algebra]]s over '''R''' are the réals, the complex numbers, and the quaternions.
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Numbers should be distinguished from ''[[numeral]]s'', which are (combinations of) [[symbol]]s used to represent numbers. The notation of numbers as a series of digits is discussed in [[numeral system]]s.

People like to assign numbers to objects in order to have unique names. There are various [[numbering scheme]]s for doing so.

Many [[language]]s have the concept of [[grammatical number]], an attribute of certain words and phrases that affects their syntactic usage and meaning.

== Extensions ==

Hasil nu paling anyar diana panalungtikan wilangan nyaéta [[hyperreal numbers]] jeung [[surreal numbers]], numangrupakeun perluasan tina wilangan nyata by adding infinitesimal and infinitely large numbers. While (most) real numbers have infinitely long expansions to the right of the decimal point, one can also try to allow for infinitely long expansions to the left, leading to the [[p-adic numbers]]. For dealing with infinite collections, the natural numbers have been generalized to the [[ordinal number|ordinal numbers]] and to the [[cardinal number|cardinal numbers]]. The former give the ordering of the collection, the latter its size. (For the finite case, the ordinal and cardinal numbers are equivalent; they diverge in the infinite case.)

The arithmetical operations of numbers, such as [[addition]], [[subtraction]], [[multiplication]] and [[division]], are generalized in the branch of [[mathematics]] called [[abstract algebra]]; one obtains the [[group (mathematics)|group]]s, [[ring (algebra)|ring]]s and [[field (mathematics)|field]]s.

== Biological basis of culture-free similarities ==

In many cultures, the notation for the numbers ''one'', ''two'', and ''three'' is very similar. In Roman numerals, the corresponding numerals are I, II, and III, and in Chinese, the same notation is used but with the tally marks written horizontally.

However, neither the Roman nor the Chinese systems use simple tally marks for ''four''.  The  Roman numeral for ''four'' is IV, meaning one less than V, which stands for ''five''. Evidently, five has significance because of the number of digits on each human hand. However, there is more here than mere human anatomy. Psychologists explain that the reason for the shift from a simple tally notation to one involving more symbols is the difficulty humans have in visually separating similar patterns with more than three identical elements. For example, it's hard to tell at a glance which is greater: IIIIIIII, or IIIIIII, but it is easy to tell X from XI.

The Arabic numeral system uses modified tally marks for 1, 2, and 3: ''1'' has undergone only very minor modification, and ''2'' and ''3'' are evidently based on horizontal lines written without lifting the pen. And again, the simple tally is abandoned with the numeral for ''4''.

== Particular numbers ==

See: [[List of numbers]], [[mathematical constant]]s, [[even and odd numbers]], [[negative and non-negative numbers]], [[small number]]s, [[large number]]s, [[orders of magnitude (numbers)]], [[prime number]]s; [[umpteen]]

== Tempo ogé ==
* [[Grammatical number]]
* [[Numbers in various languages]]
* [[Subitizing and counting]]-->

== Tumbu kaluar ==
* [http://wiktionary.org/wiki/Number Wiktionary article on ''number'']
* [http://www.stetson.edu/~efriedma/numbers.html What's special about this number?] {{Webarchive|url=https://web.archive.org/web/20180223062027/http://www2.stetson.edu/~efriedma/numbers.html |date=2018-02-23 }}

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[[Kategori:Téori kelompok]]
[[Kategori:Wilangan]]