Saturday, 7 September 2013

elementary set theory - Is an Uncountable Set and a Continuous Set the Same Thing?

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


No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...