I speak Esperanto, in which the number system goes like this:
0-9: nulo, unu, du, tri, kvar, kvin, ses, sep, ok, nau, dek
10-19: dek-unu, dek-du, dek-tri, dek-kvar, dek-kvin, dek-ses, dek-sep,
dek-ok, dek-nau
20-29: dudek-unu, dudek-du, dudek-tri, etc.
....
100-109: cent, cent-unu, cent-du, cent-tri, etc.
...
1000-1009: mil, mil-unu, mil-du, mil-tri, etc.
2012 = du mil dek du
I'm told that Japanese has a similar simple way of naming the integers.
Bruce
On Mon, Oct 8, 2012 at 5:28 PM, Dean Gerber <pd_ger...@yahoo.com> wrote:
> I don't think so. The original point (2500 years ago ?) was and still is
> to have a compact notation for the natural numbers that avoids the problem
> of naming all or at a least large number of them individually. In English
> we name the first few numbers individually: zero, one, two, three ... ten,
> eleven, twelve, at which point we begin to notice that this is becoming
> cumbersome. We wobble on to the equivalent , three-teen, four-teen,
> five-teen, ... nine-teen, and then get more and more rational and closer
> and closer to a positional system as the numbers get ever larger. We can
> at least always figure the value of our names once we have mastered the art
> of combining a small number of basic words:
>
> one two three ...nineteen
>
> twenty thirty .. .ninety (we are getting there: twenty = two-tens, thirty
> = three-tens, etc)
>
> hundred, thousand, million, billion, trillion, quadrillion ...
>
> Quick now: express 75853729915229585876325067 in "words"
>
> The point of positional notation is to use a very small set of atomic
> symbols, the "numerals", say N of them, which form an ordered sequence
> that "names" the first N-1 natural numbers 0, 1, 2, ... , N-1 (N some
> definite natural number, "two", "ten", sixteen", "sixty" etc., the "base").
> The natural numbers are then symbolized by strings of these numerals. The
> value assigned to any particular numeral in a particular position within a
> string is that numeral times the base raised to the power of that numeral's
> position in the string (positions in the string are indexed right to left
> by the natural numbers starting at 0 at the rightmost position). The value
> of the string as whole is the sum of the all values assigned to each
> particular numeral at its particular position.
>
> 1. The simplest notation: binary - base 2, numerals {0,1}.
> 2. Common early computer world: octal - base 8, numerals {0 ... 7}.
> 3. Most common modern: decimal - base 10, numerals {0 ... 9}
> 4. Modern computer world: hexadecimal (senidenary) - base 16, numerals
> {0 ... 9 a b c d e f}
> 5. Most incredible: sexagesimal (Babylonian): - base 60, numerals {
> ingenious! value of each numeral can be derived from its symbol}
>
> All Babylonian children had to memorize the multiplication and addition
> tables or Be Left Behind [image: ;) winking]
>
> Much follows from this incredible idea. We can create rational and even
> real numbers out of the notation by adding to our set of numerals the point
> symbol ( usually ".") and assigning negative powers of the base to the
> positions right of the point. All of our algorithms for adding,
> subtracting, multiplying and dividing numbers are consequences of the
> positional notation.
>
> Joshua Thorp is exactly correct. The formula he presents is the very
> elementary formula for the sum of a finite geometric series.
>
> Dean Gerber
>
>
>
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