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I did not mention Arabic numerals at all in my comment; I think you have missed my point entirely. I was actually thinking of sequences of symbols like "lim(inf

I did not mention Arabic numerals at all in my comment; I think you have missed my point entirely. I was actually thinking of sequences of symbols like "lim(inf, (1 + 1/x)^x)" being a name for e. And all algebraic numbers can be expressed by a polynomial equation and a description of which root you are referring to. Given that I literally wasn't even thinking about Arabic numerals, I was not describing a limitation of them. The limitation is with math. When talking about numbers you need a way to write down a specific number (Needs a finite representation). If it can be put into a computer, that finite representation comes from some countable set. There are uncountably many real numbers. That means we cannot given a computer understandable name to every real number. You can give a name to every algebraic number or rational number. That is a key difference that is not tied in any way to Arabic numerals.

dragontamer 4y ago
> When talking about numbers you need a way to write down a specific number (Needs a finite representation) There are plenty of rational numbers that cannot be written down. Indeed, an infinite number of them. All the numbers larger than say... a googleplex, or the numbers approaching Grahams' number (or larger than that number) are unwritable. We don't even need to stray from the integer numbers if we want to get to unwritable numbers. Plenty of numbers too large to be ever written down even if we use every single atom in our universe (or any such combination of atomic-states with all the atoms in our universe). "X cannot be written" seems to be a rather arbitrary limit.