Examples of using Finitely in English and their translations into Vietnamese
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Colloquial
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Ecclesiastic
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Computer
We claim that this process stops after finitely many steps.
(a) After finitely many of the above operations there are three balls left in the box.
Can be satisfied by only finitely many rational numbers p/q.
Stochastic matrices are used to define Markov chains with finitely many states.
For example, in chess, again, there's finitely many board positions, and finitely many things you can do.
This hints to the fact that we can precisely denote only a few,selected real numbers with finitely many symbols.
Swan's theorem states that this module is finitely generated and projective over C∞(M).
When a function is undefined at finitely many interior points of an interval, the improper integral over the interval is defined as the sum of the improper integrals over the intervals between these points.
A cover of X is said to be point finite if everypoint of X is contained in only finitely many sets in the cover.
A presentation is said to be finitely generated if S is finite and finitely related if R is finite.
Note the image under g of the standard basis generates M. In particular, if J is finite,then M is a finitely generated module.
The structure theorem for finitely generated modules over a principal ideal domain usually appears in the following two forms.
A cover of X is said to be locally finite if every point ofX has a neighborhood which intersects only finitely many sets in the cover.
A discrete environment is one where you have finitely many action choices, and finitely many things you can sense.
Examples of compact metric spaces include the closed interval[0,1] with the absolute value metric,all metric spaces with finitely many points, and the Cantor set.
It is also discrete because there's finitely many action choices and finitely many board positions, and obviously, it is adversarial, since your opponent is out to get you.
Real constructible numbers are, by definition, lengths of line segments that can be constructed from the points 0 and1 in finitely many steps using only compass and straightedge.
A group is finitely generated(respectively finitely related, finitely presented) if it has a presentation that is finitely generated(respectively finitely related, a finite presentation).
The general approach of diophantine geometry is illustrated by Faltings's theorem(a conjecture of L. J. Mordell) stating that an algebraic curve C of genus ggt;1 over the rational numbers has only finitely many rational points.
Even without using the Einstein equations, I can show that,in general, a finitely generated horizon will contain a light ray that actually meets up with itself- that is, a light ray that keeps coming back to the same point over and over again.
An extension E/F is also sometimes said to be simply finite if it is a finite extension; this should not beconfused with the fields themselves being finite fields(fields with finitely many elements).
Although Ω is easily defined,in any consistent axiomatizable theory one can only compute finitely many digits of Ω, so it is in some sense unknowable, providing an absolute limit on knowledge that is reminiscent of Gödel's Incompleteness Theorem.
For every finitely generated module M over a principal ideal domain R, there is a unique decreasing sequence of proper ideals( d 1)⊇( d 2)⊇⋯⊇( d n){\displaystyle(d_{1})\supseteq(d_{2})\supseteq\cdots\supseteq(d_{n})} such that M is isomorphic to the sum of cyclic modules.
First, Georg Cantor proved that if a trigonometric series is convergent to a function f( x){\displaystyle f(x)} on the interval[ 0, 2 π]{\displaystyle[0,2\pi]}, which is identically zero, or more generally,is nonzero on at most finitely many points, then the coefficients of the series are all zero.[1].
We are thus led to assume that, if we see two finitely different appearances at two different times, and if we have reason to regard them as belonging to the same thing, then there was a continuous series of intermediate states of that thing during the time when we were not observing it.
A theory about a topic is usually a first-order logic together with a specified domain of discourse over which the quantified variables range, finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axioms believed to hold for those things.
In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain(PID) can be uniquely decomposed in much the same way that integers have a prime factorization.