Sentence examples for place selection from inspiring English sources

He then defines a random sequence as one such that every infinite subsequence selected by an admissible place selection retains the same relative digit frequencies as in the original sequence (so one cannot select a biased subsequence, indicating that this is a genuine property of stochasticity).

But it follows from our observations about von Mises randomness (which is still a necessary condition on randomness) that no effectively computable sequence is random (if it were, there would be a place selection definable from the algorithm that selected all the 1s in the sequence).

Once this correlation takes place, selection favours those females who are able to choose the "most fit" males.

Church (1940) renders precise the notion of a place selection as a recursive function.

If the limit frequency of a digit is 1, say in the sequence 111…, it is true that every admissible place selection determines a subsequence with the same limit frequency.

If φ is an effectively computable (recursive) place selection, the compound test of first applying φ and then some recursive significance test is also a recursive significance test (since the class of recursive functions is closed under functional composition).

Church therefore imposes the condition that the admissible place selections should be, not arbitrary functions, but effectively computable functions of the preceding outcomes in a sequence.

So there is a Schnorr random sequence that does not have invariant subsequence frequencies under admissible place selections, and is therefore susceptible to exploitation by a gambling system.

As such, Ville-style sequences seem to permit successful gambling, despite the fact that they do not permit a system to be formulated in terms of place selections.

Therefore the class of ML-random sequences is closed under effective place selections, and contains only sequences with the right limit relative frequencies.

This clearly violates von Mises' intentions, as he presumably intended that the place selections should be constructively specified, yet the notion of vM-randomness remains tantalisingly vague without some more concrete specification.