I can’t believe i’m reading this…explaining this to you is like talking to a kindergartner. Don’t you see how irrelevant the symbol on the die is? It represents a number…when that face of the die lands facing up, you read the symbol and interpret it as the number you see. Again, Duh.

You damn well can distinguish succesive throws. Instead of recording 1 data point for each throw (the value), you record 2. the first data point holds the throw #, and and the second holds it’s value (1,2,3,4,5 or 6). Now you can easily distinguish throws that are the same value. Oddly, this is both obvious and intuititive for anyone but you.

You took 2 paragraphs to explain that there are a finite number of positions in a stick? a stick’s size is quantized because it can only be made from a whole # of atoms.

The only meaningful conclusion I can draw from your posts is that a real life function must choose from a finite set because you can’t physically represent an infinite # of digits. That is a true, if basic conclusion. However, that doesn’t influence how random the number coming fro the function is. The set does not represent all possible values, but randomness is not defined with respect ot all possible values, hence the dice example. a die has only 6 values, but it can generate a random number within that set.

This is a lot like saying that math exists for a machine that will never gain entropy, but you can never build it. It’s true, but it’s nothing stunning or orignial.