Given infinite time, is it possible to randomly draw a rational (instead of an irrational) from the interval [0, 1]? And if so, is it possible infinite times?
Finally, a well-formed question to which the answer "42 (times)" is a possible solution.
Certainly! Probability 0 does not mean impossible.
In this case it does. Describe any effective measure to pick a random sample from the interval and you will have cheated into choosing from the computable reals instead (of which there is a countable amount)
I don't think that's correct. You're describing a limitation of our physical computing devices (or perhaps physical reality itself) as opposed to a theoretical flaw. At least as far as I can tell.
Measure 0 is different than empty.
"Randomly" drawing anything from [0,1] is already quite difficult.
You could draw a line, or a Cantor dust. ;)
Your answer to that will depend on whether you think that is part of "all things possible."
Or, there is no time. Awareness traverses the grand graph of possibility.
Disclaimer: total armchair philosophy.
What does "traversing" even mean if there's no time?