The Infinity-Sided Die is a paradox. When you roll it, it eventually has to stop. Or if not, say you force it to, ignoring how. What number would it land on? The odds are it would land on a number bigger than any ever defined. This die is impossible to construct in real life, due to there being a limit to how small we can make things (atoms) along with how big we can make things. (common sense)
If you have a counter, and the chance of it stopping on a number N is 1 in N, And it passed the number 100, How far would it go before it's stopped? The chances that it ever stops is 100%, but again, the number it would stop on would be bigger than any number defined. And you could not make this due to processing power not being infinite. Another paradox.
These are examples of easy ways to make endless stream of random digits, although Pi has a endless stream of pseudo-random digits. If you roll this die and realize that there is a equal chance which Pi includes that, then guess what? You know the deal, same kind of paradox.
Infinity-sided dices can be used to prove pseudo-random generators can't generate all of those numbers from a infinitely large range. Only Gerald knows that proof, because two reasons: First, he's transfinitely ascended beyond The Official Hierarchy, and second, there may be a technology for true random generators in the deep layers of The Core of Everything, although nobody could achieve that from The Suprematism.