If I generate a random float value between 0…1, say to 40 digits, or n digits, aren't the chances of getting a true zero (0) or a true one (1) incredibly small? On the zero condition, every 0–9 digit has to be zero, and on the one condition, the first integer must be one and the rest should default to zero.
Does that logic of how a number is represented factor in to how random numbers are generated, or otherwise influence how unlikely that result is?
I don't have great insight into the scope of how random numbers are generated. If you ask, "What is your definition of a random number?" assume a generated digit could exhibit statistical randomness.
If I generated numbers within a range, say 5…8, aren't all integer-value results [5,6,7,8] very unlikely as well?
Note: This whole question has no intended application; I am just curious. This question was partly influenced by the mathematical elaborations of ViHart on Youtube, specifically Proof some infinities are bigger than other infinities, and extra-specifically Cantor's diagonal argument.
P.S. If any moderators want to move this question elsewhere, that's okay with me!