Steve Minutillo :: messy-78messy things

4 Comments

isis isis  

September 18th, 2003
REPLY))

what is a non-positional system ?

I always think numbers as follows:

十一–> 一十一—>1×10+1
二十–> 二十零—>2×10+0
九十九–> 九十九—>9×10+9

1^F




stevesteve  

September 18th, 2003
REPLY))

The \”arabic\” numbers are positional. The value of a number is determined only by its position.

1234 = 1×1000 + 2×100 + 3×30 + 4

1001 = 1×1000 + 1

The Chinese number system is not positional, because the values of the numbers don\’t depend solely on their position. Like in your example above:

九十九 = 9×10 + 9

Or to make it even more obvious, how would you write 10001?

一萬零一 = 1×10000 + 1

See that the value is not determined by the position? The context that a digit appears in determines its value.

Another non-positional system is roman numerals. If you just see a \”V\” four places from the right, you don\’t have any idea what the value is without looking at the rest of the number. In arabic numerals, a 5 four places from the right always means 5×1000.

2^F




WaldeWalde  

September 19th, 2003
REPLY))

Stevie, when do powers of 10 stop getting unique characters? They do, right? Otherwise that would be pretty weak. I like the idea that there are adding characters (1 through 9) and multiplying characters (powers of 10). I\’d be even more impressed if the character for 10^n looked exactly like the character for n with some extra bit that marked it as a power of 10. What\’s the deal with decimals (said in best Seinfeld voice possible)?

3^F




stevesteve  

September 19th, 2003
REPLY))

You should refer to my page of Ridiculously Large Chinese Numbers! There are unique names for 10, 100, 1,000 and 10,000. After ten thousand, there is a new name every 10,000. You say

10,000
10 10,000
100 10,000
1000 10,000

And then for 10,000 10,000 there\’s a new word. It works like that all the way up to 1,000,000,000,000,
000,000,000,000,000,
000,000,000,000,000,
000,000,000,000,000,
000,000,000,000,000.

4^F