An Uncountable set is a set that has no existence of bijection with $Z$.
Is it the same as a continuous set?
Suppose $[0,1]$ is both uncountable and continuous.
If both are different, please provide an example to clarify it.
Background: I got this doubt because of the following statement from Introduction To Probability by Dimitri P. Bertsekas
Probabilistic models with continuous sample spaces differ from their discrete counterparts in that the probabilities of the single-element events may not be sufficient to characterize the probability law