You can already represent infinitely many numbers with a finite set of symbols without positional notation, in unary. You can write "1 + 1 + 1 + 1" or "This num

You can already represent infinitely many numbers with a finite set of symbols without positional notation, in unary. You can write "1 + 1 + 1 + 1" or "This number of stars: ****" or whatever. This idea (make N marks to represent the natural number N) has surely been understood about as long as counting has been understood. The advantage of positional notation is greater efficiency at representing large numbers.