I am wondering whether any mathematical packages (i presume that there are) such as matlab, or mathematica, have the facilit/ies to prove whether or rather derive what a certain sequence converges to, if at all. For example whether (such as sequence of relative frequencies) converge to a limit as n goes infinity;
For example in the case of infinitely (countable infinite) ensembles that converge, produce their outcomes in accordance with equi-distributed sequence, whereby at each point in time, a certain algorithm, determines how the ensembles of (the same worlds) at the next point in time, produce their outcome with relation to the same sequence. I am trying to show that almost all infinitely many (countably infinite) such worlds when 'trialled', ( that is, the lim relative frequency limits to one) will give rise to countable infintie sequence within 'time' equal to particular to certain value, given my algorithms. It does not make use of expected values so I am not use of the central limit theorem will help here; it should be a purely combinatorial question. I was if there are such facilities, if likewise there is a particular coding, that I would need to use to code in an equidistributed or well distributed sequence on [0,1];
i presume I may have to pick a particular and I am supposing that I would have to encode this algorithmically, ie in virtue of an algorithm which determines what the next value will be, in virtue of what the previous ones were (or using place selection rules); that is unless, there are already packages, out there that have the facility, or the code already implicit as part of the package, in virtue of which such a sequence can be producedt
[Lim (n)->(inf) [ frequency(n) which satisfy: {(lim (t) -> inf: {(frequency (n,t, A)/t}=0.5}]/n]=1 for exampe where pr(A)=0.5 for
ie The limiting relative frequency of' a countable infinite sequence (of worlds) of countable infinite sequence (of A trials, T1,... tinf throughout time), each of whose limiting relative frequency for A over time=0.5', is 1?', where Pr(A|t) or what I call the propensity for an trial to give rise to A is 0.5 for every time and and every world.
Obviously this is not the algorithm alone, I have that; but i am wondering whether there are packages which could somehow depict, derive or notice if there are any inconsistencies with my approach to taking this limit, and which may be able to derive whether or whether there is not such a limit,
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