Inquiry: Do irrational numbers exist between 0 and 1 that can be represented without irrational numbers of an absolute value greater to one?
Conjecture: If you append the digits following the decimal in pi or e to any integer you have an irrational number. More broadly, for any irrational number k, and any integer n: k-k.floor+n is an irrational number. Can it be shown that the transfinite set of values falling between any given integers n and m does not contain a value that terminates or repeats for n+(k-k.floor)? How could it, as (k-k.floor) is by definition non-terminating and non-repeating.
e.g. The number pi -