Maddening numbers

One thing about Haiti, they use the French system of numbers (the numbers in Haitian are the same as the French numbers). Why do the French think of "80" as "four-twenty" (quatre-vingt)? And how do you suppose that affects one's number sense?

So what's so maddening about the French numbering system? And what's so maddening about ours in the US? Both systems are maddening, for different reasons and in different amounts. One thing that mathematicians like is elegance, and another thing is consistency.

Both systems are built on "base 10" -- that is, we count by tens, and we have exactly 10 digits in our systems: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

To create other numbers, we need to use place values, a decimal point, and a negative sign. With those three ideas, we can create any real number. I don't want to worry about these details, however: I just want to look at how we call numbers: the names we give to them.

For example, we need ten unique names for the ten unique digits, and both systems have those:

Numeral
English
French
0
zero
zero
1
one
un
2
two
deux
3
three
trois
4
four
quatre
5
five
cinq
6
six
six
7
seven
sept
8
eight
huit
9
nine
neuf

Each system makes two syllable mistakes, pun intended: there's no good reason to use two-syllable names for digits that will be used frequently. "zero" and "seven" are English's mistakes; "zero" and "quatre" are French mistakes.

When we speak of optimization, there are various quantities that can be optimized: for example

We can have a system which is the most efficient, the most elegant, the most beautiful, or even the ugliest!

I think of accurate and rapid communication as being important, and hence I'd recommend streamlining the language and reducing confusion. If we look at the two languages, we see that the digits are pretty well separated in terms of pronunciation -- that's a good thing, even if some of the digits are two syllables long.

Now, how to form composite numbers?

20-99

11-20

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