Any individual number has probability 0, but the probability density is the probability that you’ll get a number between x and dx, divided by dx, in the limit as dx approaches 0.
Any individual real number has the zero probability, but at least one of them—is bound to happen.
One may or may not consider sub intervals. It is a side question. Just as rational numbers, or algebraic numbers on this interval. Every sub-interval has the probability equal of its length what is always nonzero. All rational numbers have the probability 0, for example.
No, the probability density function for a uniform distribution on [0,1] is what you are integrating, and that is non-zero.
Is it? How probable is 1⁄2, for example?
That’s not what a probability density function is.
Still. How probable is 1⁄2 in the above process of coin toss?
1/2=.1000000… in the binary presentation, means one head and all tails.
Any individual number has probability 0, but the probability density is the probability that you’ll get a number between x and dx, divided by dx, in the limit as dx approaches 0.
Any individual real number has the zero probability, but at least one of them—is bound to happen.
One may or may not consider sub intervals. It is a side question. Just as rational numbers, or algebraic numbers on this interval. Every sub-interval has the probability equal of its length what is always nonzero. All rational numbers have the probability 0, for example.