3authorhave supposed that all possible sequences of any arrangement of fruits have been mapped with countable numbers, but the author can see here, that Cantor's diagonal sequence was not in those infinite fruits' sequences because it has just been created now and it is different from all those infinite sequences
at the diagonal item.
Hence, when constructing the inverse map to [PHI] we have to be careful in constructing an infinite sequence
which is 312-avoiding.
0]=0 and n taking integer values, the following infinite sequence
Using this alphabet on K letters, a feasible routing policy can be viewed as an infinite sequence
But since we are dealing with an infinite sequence
, Priest concludes that the formula is essential.
Zhang proved that like above, a certain infinite sequence
of cluster variables associated to this quiver, obtained by periodic mutation, has the property that their Laurent polynomial expansions can be expressed, under a suitable weighting scheme, in terms of perfect matchings of these subgraphs.
iii) Hypothetical frequentism: the probability of an event A in a reference class B is what the limit of the relative frequency of A's among the B's would be hypothetically if the actual (finite) sequence were extended to an infinite sequence
Let M be a Turing machine which, without ever stopping, writes the one-way infinite sequence
Informally, the difference between a task and a super-task is that a task consists of a finite sequence of actions, while a super-task consists of an infinite sequence
More precisely, let K be an infinite sequence
of numbers in [N.
Milne has shown  that the calculus of upper and lower probabilities has, mutatis mutandis, also the same dual interpretation as the standard probability calculus, both as a system of consistency constraints on belief, and as limits of long-run relative frequencies, in the latter case the limits supremum and infimum respectively of the relative frequencies of a particular character in an infinite sequence
The set of roots of (32) contains four infinite sequences
of complex roots :
His topics include finite-parameter models, infinite sequences
and discrete filters, transmission tomography, signal detection and estimation, reconstruction in Hilbert space, and reverberation and echo cancellation.
The hyperreals can be constructed as countably infinite sequences
of reals in such a way as to satisfy the above axioms.
The systems are described by infinite matrices whose rows have only finitely many nonzero elements and the state space consists of all infinite sequences