Révisi nurutkeun 7 Maret 2013 20.01 édit Addbot (obrolan \| kontribusi) 17.752 suntingan m Bot: Migrating 42 interwiki links, now provided by Wikidata on d:q185148 (translate me) ← Éditan saméméhna		Révisi nurutkeun 27 Juli 2016 15.33 édit bolaykeun Ilham.nurwansah (obrolan \| kontribusi) Kuncén 15.718 suntingan m Ngarapihkeun éjahan, replaced: nyaeta → nyaéta, ea → éa (6), eo → éo using AWB Éditan salajengna →
Baris ka-8: Interval '''R''' kabagi kana sababaraha tipe (''a'' jeung ''b'' wilangan nyata, ''a'' < ''b''): # (''a'',''b'') = { ''x'' \| ''a'' < ''x'' < ''b'' } # [''a'',''b''] = { ''x'' \| ''a'' ~~≤~~≤ ''x'' ~~≤~~≤ ''b'' } # [''a'',''b'') = { ''x'' \| ''a'' ~~≤~~≤ ''x'' < ''b'' } # (''a'',''b''] = { ''x'' \| ''a'' < ''x'' ~~≤~~≤ ''b'' } # (''a'',~~∞~~∞) = { ''x'' \| ''x'' > ''a'' } # [''a'',~~∞~~∞) = { ''x'' \| ''x'' ~~≥~~≥ ''a'' } # (-~~∞~~∞,''b'') = { ''x'' \| ''x'' < ''b'' } # (-~~∞~~∞,''b''] = { ''x'' \| ''x'' ~~≤~~≤ ''b'' } # (-~~∞~~∞,~~∞~~∞) = '''R''' téa, sét sakabéh [[wilangan nyata]] # {''a''} # [[sét kosong]] In ~~each~~éach case where they ~~appear~~appéar above, ''a'' and ''b'' are known as '''endpoints''' of the interval. Note that a square bracket [ or ] indicates that the endpoint is included in the interval, while a round bracket ( or ) indicates that it is not. For more information about the notation used above, see [[Naive set theory]]. Baris ka-30: Interval (10) is also known as a '''singleton'''. The '''length''' of the bounded intervals (1), (2), (3), (4) is ''b''-''a'' in ~~each~~éach case. The '''total length''' of a [[sequence]] of intervals is the sum of the lengths of the intervals. No allowance is made for the [[Set theoretic intersection\|intersection]] of the intervals. For instance, the total length of the [[sequence]] {(1,2),(1.5,2.5)} is 1+1=2, despite the fact that the [[Set theoretic union\|union]] of the sequence is an interval of length 1.5. Intervals play an important role in the ~~theory~~théory of [[integration]], because they are the simplest [[set]]s whose "size" or "measure" or "length" is ~~easy~~éasy to define (see above). The concept of ~~measure~~méasure can then be extended to more complicated sets, ~~leading~~léading to the [[Borel measure]] and eventually to the [[Lebesgue measure]]. Intervals are precisely the [[connectedness\|connected]] subsets of '''R'''. They are also precisely the [[convex]] subsets of '''R'''. Since a [[continuous]] image of a connected set is connected, it follows that if ''f'': '''R'''~~→~~→'''R''' is a continuous function and ''I'' is an interval, then its image ''f''(''I'') is also an interval. This is one formulation of the [[intermediate value theorem]]. Baris ka-44: In [[order theory]], one usually considers [[partially ordered set]]s. However, the above notations and definitions can immediately be applied to this general case as well. Of special interest in this general setting are intervals of the form [''a'',''b'']. For a partially ordered set (''P'', ~~≤~~≤) and two elements ''a'' and ''b'' of ''P'', one defines the set : [''a'', ''b''] = { ''x'' \| ''a'' ≤ ''x'' ≤ ''b'' } One may choose to restrict this definition to pairs of elements with the property that ''a'' ~~≤~~≤ ''b''. Alternatively, the intervals without this condition will just coincide with the [[empty set]], which in the former case would not be considered as an interval. == Interval arithmetic == Baris ka-52: '''Interval arithmetic''', also called '''interval mathematics''', '''interval analysis''', and '''interval computations''', has been introduced in 1956 by M. Warmus. It defines a set of operations which can be applied on intervals : T ~~·~~· S = { ''x'' \| there is some ''y'' in ''T'', and some ''z'' in ''S'', such that ''x'' = ''y'' ~~·~~· ''z'' } * [''a'',''b''] + [''c'',''d''] = [''a''+''c'', ''b''+''d''] Baris ka-64: ==Notasi alternatip== Cara sejen keur nuliskeun interval, ilaharna katempo di [[France]] sarta sababarha nagara Eropa sejenna, ~~nyaeta~~nyaéta: * ]''a'',''b''[ = { ''x'' \| ''a'' < ''x'' < ''b'' } * [''a'',''b''] = { ''x'' \| ''a'' ~~≤~~≤ ''x'' ~~≤~~≤ ''b'' } * [''a'',''b''[ = { ''x'' \| ''a'' ~~≤~~≤ ''x'' < ''b'' } * ]''a'',''b''] = { ''x'' \| ''a'' < ''x'' ~~≤~~≤ ''b'' } ==Tumbu kaluar== Baris ka-75: *[http://www.cs.utep.edu/interval-comp/icompwww.html Interval computations research centers] [[~~Category~~Kategori:Topology]] [[~~Category~~Kategori:Order theory]] [[Kategori:Matematika]]

Interval (matematika): Béda antarrépisi