Which is precisely what enables the positional system at the conceptual level: not only you can have "gaps" in the middle, but it enables you to distinguish between 1 and 10 and 100.

Babylonians, for example, didn't conceptualize 0 as a numeric quantity just like 1 or 5. So, when they invented a sign for gaps in the numbers, they didn't use it at the ending positions, so their "I" could mean 1, or 60, or 3600, or..., depending on the context. Neither was it used to signify the quantity of zero: empty space was used instead.

Yes, sorry, my point didn’t come across very well.

What’s quite interesting is to ask pupils to assign numbers to their fingers and thumbs:

1 2 3 4 5 6 7 8 9 ... X?

It’s a good way of introducing positional number systems, and the... paradox? quandary? quirk?.. of how base N never includes a symbol for N, and how N in base N is always ‘10’.

See also: asking pupils to divide 12345* by 67, taught in the context of arithmetic and logical shifting.

(*base 67)

You’re right. There are two types of 0: the internal syntax denoting digit shift, like in 507, and the number representing nothing, as in 0. So in our number system, o isn’t just syntax, it’s also a number.