I think my easy answer is to say that infinite numbers are not in N.  I
like to think of it with a decimal point in front, to form a number
between 0 and 1.  Yes you have the rational numbers which eventually
have a repeating pattern (or stop).  But you also have in among them
the irrational numbers which are uncountable. (Hey this reminds me of
the fi among the Fi.)

To ask what is the next number after an infinite number, like
11111...11111... is similar asking what is the next real number after


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