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baduseron How the continuum hypothesis could have been a fundamental axiom

> rather generate a number

How?

baduseron How the continuum hypothesis could have been a fundamental axiom

If you picked that, you did not pick uniformly from the unit interval. You picked from something else, which was much smaller.

baduseron How the continuum hypothesis could have been a fundamental axiom

I guess, but, the set is not even countably infinite. "Selecting at random" is something that happens in the real, non-infinite world, not in the mathematically rigorous would where infinities can exist. So, no, probability-zero events do not happen in either.

baduseron How the continuum hypothesis could have been a fundamental axiom

> Probability-zero events happen all the time. The probability of getting any specific value selected uniformly at random from the unit interval (say, 0.232829) is zero.

I would strongly challenge that claim. First, you did not choose that number uniformly at random, you chose it from at best a countably infinite subset, or more realistically, from a finite subset. And secondly, I do not think you can describe a situation where a number is actually chosen uniformly and randomly from the unity interval.