> This always seemed wildly implausible to me. A very large number of communicable meanings, sure, but infinite?
This is "trivial" in the boring kind of way. With just digits, we can communicate an infinite set of distinct numbers simply by counting.
We can't really communicate an infinite amount of numbers. People just can't read or remember too many digits.
We can. Scientific notation with 1 significant figure can be meaningful because we can use it to figure out order relations. It’s an infinite language.