What is the difference between something being "true" and 'true with probability 1"? In the beginning of chapter 2 of Information Theory, Inference and Algorithms, the author says that he will refrain from being unnecessarily rigorous and provides the example of saying that something is "true" instead of saying more formally that said thing is "true with probability 1".
Is there a difference between something being "true" and 'true with probability 1" ?

Consider the (-1,-1)-(+1,+1) sheet with a point sized hole in the origin.
It is true with probability 1 that a random point within (-1,-1)-(+1,+1) in the sheet. But there is a point that meets that definition that isn't on the sheet. So it is not true that a point within (-1,-1)-(+1,+1) is on the sheet.
There is no difference in the finite realm.
