I used to consider myself a math major.

I wonder if what research has been done into investigating the existence of irrational numbers between the integers. I am curious about the distribution of terminating and non-terminating repeaters relative prime numerators and denominators.

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 - pi + n is irrational for integer n.

It would be swell...

Gosh golly gee, I would really like a network of clones of my brain and a few dozen supercomputers. I wonder if anyone makes a wetware network interface yet. I have really got to plan my time travelling better. I think I am going to go see if I can play Diablo.