I am reading the (german) Applied Statistics and on page 140 as a consequence of the Kolmogorov axioms it is stated that if $P(A)=0$ one cannot conclude that $A=\emptyset$ . Similarly if $P(A)=1$ one also cannot conclude that $A=S$. Why is that?
Also, if $P(A)=0$ this means that event A is almost never possible and if $P(A)=1$ will almost surely occur.
I am having a bit of a trouble intuitively understanding the need for the above statements (almost surely or almost never) and why if $P(A)=1$ one cannot conclude that $A=S$.