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between .999... and 1:
define .999... then maybe I'll try to answer
between .9, .99, .999, ... and 1:
Take the rational functions with polynomials in their numerator and denominator with integer coefficients, with a positive leading coefficient in the denominator and no common factors between numerator and denominator. Use the usual addition and multiplication, reducing after the operation, and order them by which one is larger when x goes to infinity. This has .9, .99, .999, ... < (x-1)/x < 1 and its cardinality is aleph0.
