arbitrarily small in a sentence
1) Fine or detailed structure at arbitrarily small scales.
arbitrarily collocations
2) These converge to arbitrarily small intervals around __FORMULA__ and __FORMULA__.
3) Besicovitch showed that there are Kakeya needle sets of arbitrarily small positive measure.
arbitrarily small example sentences
4) Besicovitch's work showing such a set could have arbitrarily small measure was from 1919.5) In other words, a filter is Cauchy if it contains " arbitrarily small " sets.
6) In the case of an excited atomic nucleus, the arbitrarily small disturbance comes from quantum vacuum fluctuations.
7) Moreover, ε is an arbitrarily small positive number, and log is the logarithm to an unspecified base.
8) Thus, an arbitrarily small change, or perturbation, of the current trajectory may lead to significantly different future behavior.
9) Qualitatively a surface is positively or negatively curved according to the sign of the angle excess for arbitrarily small geodesic triangles.
10) If the radius is large enough, the two balls will coincide except for an arbitrarily small proportion of their volume.
11) If not it holds for "a" + ε1 with ε arbitrarily small and hence also in the limit.
12) Since rotations and translations of the plane can be arbitrarily small the notion arises of an (infinite) continuous group.
13) Rather, these quantities can only be determined with some characteristic 'uncertainties' that cannot become arbitrarily small simultaneously.
14) The class action rule does not prevent an arbitrarily small chance of an infinite value from smothering all considerations of finite value.
15) In particular, if a continuous function takes on arbitrarily large values and arbitrarily small values, then it is necessarily surjective.
example sentences with arbitrarily small
16) In addition, for any rate "R > C", it is impossible to transmit with arbitrarily small block error.17) There is, however, a strictly positive probability that the long term player's type lies in an arbitrarily small interval around the dominant strategy type.
18) Now, by Planck's quantum hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum.
19) In principle, by using very large "n" the RE of the estimated "g" could be driven down to an arbitrarily small value.
20) Conversely, many "solids" (even granite) will flow like liquids, albeit very slowly, even under arbitrarily small stress.
21) Although there are Kakeya needle sets of arbitrarily small positive measure and Besicovich sets of measure 0, there are no Kakeya needle sets of measure 0.
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