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...y</math> iff <math>x\preceq y</math> and <math>x\succeq y</math>) are a [[countable set]]. 2. There is a countable subset of X, <math>Z=\{z_0,z_1,...\}</math>, such that for every pair of no ...

For the case of a [[countable set|countable]] state space we put <math>i,j</math> in place of <math>x,y</math>. ...ate <math>j</math> at some later time <math> t > s </math>. The continuous quantities <math>A_{ij}(t)</math> satisfy ...

...screte-time signal''' is a [[time series]] consisting of a [[sequence]] of quantities. ...o contrast, a [[discrete time|discrete-time]] signal has a [[countable set|countable]] domain, like the [[natural number]]s. ...

...the real numbers are [[uncountable]] and the [[rational number|rationals]] countable, it follows that [[almost all]] real numbers are irrational.<ref>{{Cite boo ...not discrete collections of units; this is why ratios of incommensurable [quantities] appear... .[Q]uantities are, in other words, continuous".<ref name="Kline ...

...nciple of indifference: ''If someone is truly ignorant about a discrete or countable set of outcomes apart from their potential existence but does not assign th "Shifting" all quantities up by some number ''b'' and solving in the "shifted space" and then "shifti ...

...or|consistent]], using the [[uniform convergence]] properties of empirical quantities to their means. This technique was used to obtain generalization bounds for ...Furthermore, we assume that all functions are measurable and all sets are countable. ...

...some sense, there are ''more'' real numbers than there are elements in any countable set. ...eparable space|separable]]. This is because the set of rationals, which is countable, is [[Dense set|dense]] in the real numbers. The irrational numbers are als ...

Depending on the exact values of the quantities <math>\varepsilon_n</math>, these two operators, together with the identity ..._n = \omega\varepsilon_n</math> by introducing a sequence of dimensionless quantities <math>\{\varepsilon_n\}</math> ordered as: <math>0 = \varepsilon_0 < \varep ...

...Bernoulli|Bernoulli]])<ref name="Jesseph" /> regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathema ...nite quantities were ideal entities, not of the same nature as appreciable quantities, but enjoying the same properties in accordance with the [[Law of continuit ...

...English determiners|determiner]] used with [[Grammatical number|singular]] countable [[English nouns|nouns]], as in ''one day at a time''.{{sfn|Huddleston|Pullu ...rby|Marmodoro|2020|pp=99}} [[Dimensionless quantities]] are also known as 'quantities of dimension one'.{{sfn|Mills|1995|pp=538-539}} In [[quantum mechanics]], t ...

...ics)|Hamiltonian]]—there are no other functionally independent [[conserved quantities]] on the [[phase space]]. More explicitly, suppose that the energy {{math|' ...ormal set (or an orthonormal sequence if {{math|''B''}} is [[countable set|countable]]). Such a system is always [[linearly independent]]. ...

...as [[b:Physics with Calculus/Mechanics/Scalar and Vector Quantities|vector quantities]]; they must be dealt with using [[vector analysis]]. ...becomes useful. Statistical mechanics describes the behavior of large (but countable) numbers of particles and their interactions as a whole at the macroscopic ...

...re nonzero. In the sequel it is (for simplicity) assumed that the basis is countable, and Latin letters are used for the indices and the indexing set can be tak ...and a prime differentiation with respect to {{mvar|σ}}. A dot ''between'' quantities denotes the relativistic inner product. ...

...ers and operations. It generalizes these operations by allowing indefinite quantities in the form of variables in addition to numbers.<ref>{{multiref | {{harvnb| ...m.de/lexikon/mathematik/algebra/12062 Algebra]}} }}</ref> When used as a [[countable noun]], an algebra is [[algebra over a field|a specific type of algebraic s ...

...calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic ...|uncountably infinite]] but the set of all real [[algebraic number]]s is [[countable|countably infinite]]. [[Cantor's first uncountability proof|His proof]] doe ...

...stence of infinite entities and infinite processes, emphasizing only those quantities or procedures that are finite.}} {{defn |1=A theorem in mathematical logic that states any countable theory with an infinite model has models of all infinite cardinalities, hig ...