- #1

pob1212

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True or False: Every infinite sequence of natural numbers, who's terms are randomly ordered, must contain every possible subsequence of any length, including infinity.

For example, does the infinite and random sequence [itex]\small M[/itex] of natural numbers require that the subsequence {59,1,6} exist within it? Or the ordered set [itex]\small N[/itex] of natural numbers for that matter?

My intuition is no. We could construct a sequence [itex]\small M[/itex], as described above, then extract every sequence {59,1,6} from [itex]\small M[/itex], and still have an infinite sequence. What about the idea that since M is infinite it has infinitely many chances for any unique set (even infinite sets like [itex]\small N[/itex]) to occur within it?

Thanks,

pob