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 limit superior and limit inferior - Definition 

Limit superior and limit inferior (5206 bytes)
1: ...uperior''' of a [[sequence]] can be thought of as limiting bounds on the sequence.
3: The limit inferior (or '''lower limit''') of a sequence (''x''<sub>''n''</sub>) is defi...
11: Similarly, the limit superior (or '''upper limit''') of (''x''<sub>''n''</sub>) is defined as
19: ...rtially ordered set]], provided the [[supremum]]s and [[infimum]]s exist.
20: ...e every sequence has a limit superior and a limit inferior.

Inferior and superior planets (721 bytes)
1: The terms "'''inferior planet'''" and "'''superior planet'''" were coined by [[Nicolaus Copernicus|C...
3: ...used in reference to [[Mercury (planet)|Mercury]] and [[Venus (planet)|Venus]], which are closer to the...
5: ... (planet)|Uranus]], [[Neptune (planet)|Neptune]], and [[Pluto (planet)|Pluto]], which are farther from ...
7: ...sed more generally: for instance, the Earth is an inferior planet as seen from Mars.

Limit (607 bytes)
1: A '''limit''' can be:
3: * [[Limit (mathematics)]], including:
4: ** [[Limit of a function]]
5: ** [[Limit of a sequence]]
7: ** [[Limit (category theory)]]

No limit (158 bytes)
1: '''No limit''' may refer to:
3: #A song by [[2 Unlimited]], see [[No Limit]].
7: [[sv:No limit]]

No Limit (546 bytes)
1: ...etting (poker)]]. For the record label, see [[No Limit Records]]''
2: ... is one of the most well know [[eurodance]] songs and was a world-wide hit which still is frequently pl...
4: [[Category:1993 singles|No Limit]]
6: [[sv:No Limit]]

Liquid limit (1266 bytes)
1: ...own as the upper plastic limit, and the Atterberg limit, is the [[water]] content at which a [[soil]] cha...
3: ...under the impact of 25 blows in a standard liquid-limit apparatus.
5: ...ong]], subject to landslides. In Hong Kong liquid limit tests are performed on a regular basis to check t...
7: ...limit]] are used together for soil identification and classification.
13: [http://www.umeciv.maine.edu/cie366/atterberg_limits/default.htm Undergraduate worksheet from Univers...

Classical limit (1581 bytes)
1: ...continuity argument should apply to the classical limit of quantum systems as the value of [[Planck's con...
3: ... energies and large objects (relative to the size and energy levels of an electron) are considered in q...
5: ...ivity]], if we consider flat space, small masses, and small speeds (in comparison to the speed of light...

Speed limit (17283 bytes)
1: ...]]'s relativity theories states that the '''speed limit''' of the [[Universe]] is the [[speed of light]] ...
5: ... different units (for example, between [[Canada]] and the United States), they may be marked on the fir...
7: ...Eire_60_kmh.jpg|frame|right|New style Irish speed limit sign in km/h]]
9: ...mation on the Irish metrication of road and speed limit signs can be found at the official website: http:...
11: [[Image:Pr-pic1.jpg|thumb|right|Standard Binnacle for Automobile speedometers used in m...

Limit loads (412 bytes)
1: '''Limit load''' is the maximum load that a structure can ...
2: Any load above the limit the limit load will lead to the formation of [[plastic]] hi...
3: Engineers use limit states to define and check a structure's performance.

Limit of inquiry (1068 bytes)
1: ...uiry''' is the limits of human ability to inquire and answer questions about phenomena. In the [[20th ...
3: *The [[Planck length]] - actually a limit on [[distance]] itself.
8: The [[incompleteness theorem]] which limits the [[consistency]] or [[completeness]] of [[sym...
10: ..., and from [[uniqueness]], notably in [[ecology]] and [[psychology]].
12: ...ped by realizing that truth must conform to these limits, beyond which any concept of truth is just specu...

Roche limit (14289 bytes)
3: ...from above the orbital plane. Far from the Roche limit the mass is practically spherical.]]
5: ...mit_(tidal_sphere).PNG|framed|Closer to the Roche limit the body is deformed by [[tidal force]]s.]]
7: ...gravity can no longer withstand the tidal forces, and the body disintegrates.]]
9: |[[Image:Roche limit (top view).PNG|framed|Particles closer to the pri...
11: | [[ Image:Roche_limit_(ring).PNG|framed|The varying orbital speed of th...

Limit-cycle (1256 bytes)
1: ...]]'' limit-cycle. Otherwise it is an ''unstable'' limit-cycle.
3: ...o the limit-cycle, making the system stick to the limit-cycle.
5: [[Image:Limitcycle.jpg]]
7: ...s of this system, make the system converge to the limit cycle. Hence, this system exhibits self-sustained...
10: * Steven H. Strogatz, "Nonlinear Dynamics and Chaos", Addison Wesley publishing company, 1994.

One-sided limit (813 bytes)
1: ...thematics]], a '''one-sided limit''' is where the limit of a function is defined in moving in the positiv...
11: Now, if we take the limit moving from smaller values of ''x'' to 1, noted, ...
13: ''but'' if we take the limit moving from larger values of ''x'' to 1, noted,
16: ...ts are not identical and so ''f'' has a one-sided limit at the point ''x''=1.
18: ... are identical, ''f'' is said to have a two-sided limit at that point.

Limit cardinal (4940 bytes)
2: In [[mathematics]], '''limit cardinals''' are a type of [[cardinal number]].
4: ...also a limit cardinal if and only if &alpha; is a limit ordinal.
6: ...dinal is also (with the [[axiom of choice]]) weak limit cardinal, as we'd expect from the names, since fo...
8: ...o and &alefsym;<sub>0</sub> should be regarded as limits; some mathematicians insist that they be uncount...
10: ... letter of the [[Hebrew alphabet]]) to get strong limit cardinals such as

Eddington limit (909 bytes)
3: ...physics]], the '''Eddington Limit''' is a natural limit to the [[luminosity]] that can be radiated by sph...
5: ...e luminosity naturally decreases to the Eddington limit where gas is pushed inward again.
7: The Eddington limit is a function of the mass of the accreting object...

Limit point (4691 bytes)
2: ...as an operation that enriches a set by adding its limit points.
6: We say that a point ''x'' in ''X'' is a ''limit point'' of <var>S</var> if
7: ...rm of the definition to derive facts from a known limit point.)
10: ... <var>x</var> is a limit point of <var>S</var> if and only if it is in the [[closure (topology)|closure...
11: ...rhood of the point meets the set. Now, ''x'' is a limit point of ''S'', iff every neighbourhood of ''x'' ...

Limit (music) (1905 bytes)
1: ...tunings are properly found in barbershop singing, and a few other relatively isolated genres.
3: ...c theory literature: '''prime limit''' and '''odd limit'''. Not all authors are aware of the distinction.
5: ...d [[whole number]]. Note that prime limit and odd limit do not cover the same scales even when n is an od...
7: ...luding his famous 43-tone scale, based on a prime limit of 11.

Limit of a sequence (5619 bytes)
1: ...]. It is the essential tool in calculating [[pi]] and [[trigonometric function]]s.
5: ...is famous for formulating paradoxes that involved limiting processes.
7: ...ppus]], [[Democritus]], [[Antiphon]], [[Eudoxus]] and [[Archimedes]] developed the [[method of exhausti...
9: ...>''n''</sup> which he then linearizes by ''taking limits'' (letting ''o''&rarr;0).
11: ...ed under which conditions a series converged to a limit.

Limit of a function (10693 bytes)
3: In [[mathematics]], the '''limit of a function''' is a fundamental concept in [[ma...
5: ...er informally, to say that a function ''f'' has a limit ''y'' when ''x'' tends to a value ''x<sub>0</sub>...
7: ...opology)]] for a generalization of the concept of limit.
17: ... ''f''(''x'') is ''L'' as ''x'' approaches ''p''" and write
21: if and only if

Direct limit (5749 bytes)
1: ...s)|groups]] and [[module (mathematics)|modules]], and then the general definition which can be used in ...
7: ...]] (over a fixed field), etc. We will also understand ''[[homomorphism]]s'' in the corresponding settin...
9: ... family of objects [[index set|indexed]] by ''I'' and suppose we have a family of homomorphisms ''f''<s...
14: The '''direct limit''', ''A'', of the direct system (''A''<sub>''i''<...
20: ...gory ''C'' (same definition as above). The direct limit of this system is an object ''X'' in ''C'' togeth...

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