I suppose Roman numerals would be one counterexample, but are there any number systems based on place/position value that qualify as counterexamples?
I suppose Roman numerals would be one counterexample, but are there any number systems based on place/position value that qualify as counterexamples?
English number words are positional-ish and base 10, but have special words up to 12, as well as 100, 1000, 1000000
Of course. The Chinese number system is base 10 (or, if you scale way up, base 10,000) with a positional writing system.
The symbol for ten is 十. Heck, there's also a symbol for twenty, 廿, and it exists despite the number system being base 10. Anything that has to be written a lot is likely to have a convenient written form.
If you're curious, zero is 零. Successive zeroes are combined, so 一千零一 is 1001. 5147 would be 五千一百四十七. 10, as previously mentioned, is 十.
> Heck, there's also a symbol for twenty, 廿, and it exists despite the number system being base 10.
I'm not sure that if you intend to captured the structure of chinese symbols, you wouldn't to make the radicals something below symbols. Then 廿 wouldn't count as a single symbol here, but rather as a concatenation of two 十, i.e. the same as XX is 20 in roman numerals.
You are wrong about this. The structure of the characters is very explicit; one character per square.
(As a matter of character etymology, you are right that 廿 and its variant form 卄 come from combining two 十. But that can't make it "two symbols".)
> 5147 would be 五千一百四十七
"Five thousand one hundred four tens seven". So each order of magnitude is explicitly labeled. Where's the positional part?
That is the positional part. If you were to rearrange it, you'd get something invalid. 二十三百 isn't a number at all.
Recall that the use of zero is necessitated by using positional notation, and that's just as true here: you must explicitly zero any magnitudes you're not using. (At least, any that are below one you are using.)