Thanks for the responses ladies and gents After reading through your replies and a1call's linked page, I *think* I got it. The probability of getting an integer (or any other number) from the hypothetical perfect RNG is simply 1/infinity, an infinitely small number tending to, but *not* equal to, zero. The way I "visualize" this is that as I run (execute, crank through) the RNG more and more times, the ratio of integers versus real numbers will continue to decrease and converge on zero. The same way that as I flip a coin more and more times, the ratio of heads to tails will converge to 1:1.

Ken G, in belated response to your question, I was thinking that the hypothetical perfect RNG would have infinite precision on both the left hand side and the right hand side of the decimal point. As you said, if there is one decimal point precision, the odds would be 1/10, if there are two, the odds would be 1/100. So given infinite precision on the RHS, the odds should be (if I'm thinking about this correctly) 1/infinity. Same result as above, slightly different path. Which I take to be a good sign; if the two reasoning gave different results, my noodles would really be baked!

Thank you, everyone, for humoring me