Discuss reasons why the Hindu Arabic numeration system is superior to other ancient numeration systems.

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Here are some number systems to consider:

(1) Babylonian/Sumerian: Used base 60 for measurement and astronomy but base 10 for accounting purposes. This number system is the first to use positional notation (the numerical value for a sign depends on its position; in Hindu-Arabic notation this is equivalent to noting that the 2 in 12 indicates 2 ones, while the 2 in 21 indicates 2 10s). This system disappeared around 550 BCE.

(2) Chinese: Used base 10, but was not positional. Thus you could write the characters for 423 in any orientation as there was a symbol for 423 which could not be mistaken for another number. The symbols used were essentially the symbols for the words indicated by the number.

(3) Mayan: Used a base 20 system. (Some modern romance languages, such as French, have a vestigial base 20 -- e.g. 84 is 4 twenties and a 4.) This system was positional and included a zero. Addition and subtraction were easy as you added dots or bars. This was in the New World so had no effect on Europe or Asia or Africa.

(4) Egyptian: Used a base 10 system without a zero. This was not a place value system. In the hieratic system there was a zero, and there was a place value. This system was used by accountants. Each number from 1-9 was represented by a letter (this idea was adopted by the ancient Greeks).

(5) Greek: Used a base 10 (decimal) system; it was not positional. Letters were used for numbers (later with a bar to indicate use as a number). There was no zero except for use in fractions.

(6) Roman: Used base 10; it was not positional.

The Hindu-Arabic system is base 10, positional, and uses zero as a number and a place-holder. This simplifies basic arithmetic, especially multiplication. Most of the other systems either lacked a place-holder (causing potential confusion with the numbers) or were not positional (making arithmetic hard).

The symbols used in the Hindu-Arabic system are not letters, so numbers are not confused with words (as would be possible in Greek or Egyptian numbers).

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