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ARBITRARILY
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- In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
- More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument.
- Additionally, comparisons are complicated because place names may be considered words, technical terms may be arbitrarily long, and the addition of suffixes and prefixes may extend the length of words to create grammatically correct but unused or novel words.
- Since the definition of an extreme environment is relative to an arbitrarily defined standard, often an anthropocentric one, these organisms can be considered ecologically dominant in the evolutionary history of the planet.
- In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension.
- Representing the state of a robot with traditional first-order logic requires the use of many axioms that simply imply that things in the environment do not change arbitrarily.
- Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones (while having at least one value unchanged).
- Existence monism posits that, strictly speaking, there exists only a single thing, the universe, which can only be artificially and arbitrarily divided into many things.
- This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length.
- Pumping lemma for regular languages, the fact that all sufficiently long strings in such a language have a substring that can be repeated arbitrarily many times, usually used to prove that certain languages are not regular.
- Empirical distributions can only fit a power law for a limited range of values, because a pure power law would allow for arbitrarily large or small values.
- Unlike many other text formatters, troff can position characters arbitrarily on a page, even overlapping them, and has a fully programmable input language.
- One can interpret this measurement as a computation on 1 bit for this system; however, Bremermann's limit is difficult to interpret physically, since there exist quantum Hamiltonians for which this interpretation would give arbitrarily fast computation speeds at arbitrarily low energy.
- Six Degrees of Kevin Bacon or Bacon's Law is a parlor game where players challenge each other to arbitrarily choose an actor and then connect them to another actor via a film that both actors have appeared in together, repeating this process to try to find the shortest path that ultimately leads to prolific American actor Kevin Bacon.
- The ed text editor (also authored by Thompson) had regular expression support but could not be used to search through such a large amount of text, as it loaded the entire file into memory to enable random access editing, so Thompson excerpted that regexp code into a standalone tool which would instead process arbitrarily long files sequentially without buffering too much into memory.
- In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth.
- Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory.
- Rich wrote that a colonel working in the Pentagon arbitrarily assigned the name "Aurora" to the funding for the B-2 bomber design competition and somehow the name was leaked to the media.
- A prime meridian is an arbitrarily chosen meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°.
- Unlike the concept of UNIX mount points, where volumes are named and located arbitrarily in a single hierarchical namespace, drive letter assignment allows multiple highest-level namespaces.
- Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.
- Using many parts can set the exponent arbitrarily close to 1, but the constant factor also grows, making it impractical.
- Geometry is founded on arbitrarily chosen axioms - there are infinitely many equally true geometries.
- To prevent interference between different users, the artificial generation and use of radio waves is strictly regulated by law, coordinated by an international body called the International Telecommunication Union (ITU), which defines radio waves as "electromagnetic waves of frequencies arbitrarily lower than , propagated in space without artificial guide".
- Calhoun, land commissioner of the Illinois Central Railroad, by arbitrarily combining single consonants and vowels.
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