I have just started learning probability course and my professor said something really strange.
If we take a random real number between 0 and 1 (including) then the chance of getting 1/2 is 0
The chance of getting a number in [0,1/2] is 1/2
While I totally agree with the second point I don't agree with the first one.
I know that the chance is really really small since there are non countable real numbers between 0 and 1 but saying that the probability is 0 means that you will never get 1/2 but that is not true since 1/2 is a possible chance.