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...s]], the particle number is a [[dimensionless quantity]], specifically a [[countable quantity]]. It is an [[extensive property]], as it is directly proportional [[Category:Countable quantities]] ...

{{short description|Degree of concentration of countable objects}} ...intensive quantity]] used to describe the degree of [[concentration]] of [[countable]] objects ([[Elementary particle|particle]]s, [[molecules]], [[phonon]]s, [ ...

{{Short description|Words that measure quantities}}{{About|measure words in general|measure words in Chinese|Chinese classifi ...makes it clear the fraction must be a noun referring to a part of another countable noun. ...

(interpret the quantities as [[cardinal numbers]] if some of them are infinite). ...ble]] or [[Uncountable set|uncountable]], depending on whether ''H'' has a countable number of cosets in ''G''. Note that the index of ''H'' is at most the orde ...

...f> Typically expressed as [[ratio]]s that align with another system, these quantities do not necessitate explicitly defined [[Unit of measurement|units]]. For in ...e+the+unitless+ratios+in+limits+or+derivatives+often+involve+dimensionless+quantities&pg=PP1 |title=EBOOK: Fluid Mechanics Fundamentals and Applications (SI unit ...

...'s work does not contain specific numbers mapped onto lines, only abstract quantities.<ref>Núñez, Rafael (2017). [https://web.archive.org/web/20200129052058/http ...of [[rational number]]s. It is a theorem that any linear continuum with a countable dense subset and no maximum or minimum element is [[order-isomorphic]] to t ...

..., ''information'', ''physics''. However, many nouns of this type also have countable meanings or other contexts in which a plural can be used; for example ''wat ...', ''101 dogs'', ''four and a half hours'') and for unspecified amounts of countable things (''some men'', ''several cakes'', ''how many lumps?'', ''birds have ...

...population ecology]], '''population size''' (usually denoted ''N'') is a [[countable quantity]] representing the number of individual [[organism]]s in a [[popul [[Category:Countable quantities]] ...

# <math>P(X \in \bigcup_{i} E_i ) = \sum_i P(X \in E_i)</math> for any countable disjoint family of sets <math>\{ E_i \}</math> ...the probability distribution of a random variable that can take on only a countable number of values<ref>{{Cite book |last=Erhan |first=Çınlar |author-link=Erh ...

...]'' can be defined by replacing mass by [[number of particles]] or other [[countable quantity]], with resulting units of m⁻². [[Category:Area-specific quantities]] ...

...trength'' is uncountable in ''Strength is power'', but it can be used as a countable noun to mean an ''instance'' of [a ''kind'' of] strength, as in ''My streng ...ne-''singular'' pair-''singular'' glasses-''genitive plural''). For larger quantities, "collective numeral" forms are available: {{lang|pl|troje drzwi}} (three d ...

...lternatives to theory <math>T</math>. For this equation to make sense, the quantities <math>\mathbb P[D|T]</math> and <math>\mathbb P[D|A]</math> must be well-de ...ributions is a subset of the set of all programs, which is [[Countable set|countable]]. Similarly, the sets of observable data considered by Solomonoff were fin ...

...n to be automatically valued in the real numbers, with more general random quantities instead being called ''[[random element]]s''. ...[[Image (mathematics)|image]] (or range) of <math>X</math> is finite or [[countable set|countably]] infinite, the random variable is called a '''discrete rando ...

==Finite vs. countable sets of generators== ...[[quantum field theory]] the following [[Gaussian integral]] of Grassmann quantities is needed for fermionic anticommuting fields, with ''A'' being an ''N''&nbs ...

...erminism|non-deterministic]] or uncertain processes or measured [[Quantity|quantities]] that may either be single occurrences or evolve over time in a random fas ...heory; but, alternatives exist, such as the adoption of finite rather than countable additivity by [[Bruno de Finetti]].<ref>{{cite web|url=http://www.probabili ...

...g the few expressions of [[statistical mechanics]] where the thermodynamic quantities defined in the quantum case find no analogous definition in the classical l ...sub>'', each treated as a microstate. Now the microstates are discrete and countable<ref>{{Cite web| url=https://web.stanford.edu/~peastman/statmech/statistical ...

In the [[thermodynamic limit]], the fluctuation of the macroscopic quantities from their average values becomes negligible; so this reproduces the defini ...rom a completely isolated system to a system that can exchange one or more quantities with a reservoir, like energy, volume or molecules. In every ensemble, the ...

Informal notations for non-real quantities have historically appeared in calculus in two contexts: as infinitesimals, ...erreal system; infinite quantities differ in magnitude from other infinite quantities, and infinitesimals from other infinitesimals. ...

.... random variables. That is, there are underlying, generally unobservable, quantities that are i.i.d. – exchangeable sequences are mixtures of i.i.d. sequences. ...Borel space]], and consider the space of sequences on <math>X</math>, the countable product <math>X^\mathbb{N}</math> (equipped with the [[product sigma-algebr ...

* The '''lattice''': A countable set <math>\mathbb{L}</math>. To help understand the above definitions, here are the corresponding quantities in the important example of the [[Ising model]] with nearest-neighbor inter ...