Regarding convergence, only a topology is required, and assuming a finite alphabet A with the discrete topology, the space of infinite strings J takes on the topology of the direct product J = A x A x A x . . .. This makes J homeomorphic to the Cantor set, and is of course unchanged under any permutation of the factors. This topology can be realized by a metric, but unfortunately there's a loss of symmetry: I don't think there's any metric such that all self-homeomorphisms are isometries. One metric realizing the above topology -- so at least convergence in the metric equals convergence in the topology -- is to let the nth alphabet factor have all pairs of letters at a distance of 1/n, and then to define distance by the usual Euclidean formula -- square root of sum of squares of distances in all factors. Of course the maximum possible distance is then pi/sqrt(6). --Dan Marc wrote: << . . . I'm trying to grok processes where infinite strings can be said to converge element-wise, but the strings themselves are only roughly inter-related--having Hamming distance, but no meaningful lexical order.

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele