The decimal expansion of any irrational number x>0 is non-repeating. This is well known. So, we have a way of obtaining irrational numbers, such hasx=0.101101110111101111101…(after the decimal point, we have one 1, one 0, two 1's, one 0, three 1's, one 0, and so on).
My (admittedly vague) question is this: how to obtain a known irrational number whose decimal expansion (or, for that matter, whose expansion on some base) is easily shown to be non-repeating? Of course, when I write that that the decimal expansion “is easily shown to be non-repeating” what I mean is that it is easy to describe its decimal expansion (and to see that it is non-repeating); otherwise, one could just say that, since the number is irrational, its decimal expansion must be non-repeating. And by “known number” I mean something like, say, 3√2 or πe.
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