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Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago.
Roman and East Asian abacuses use a system resembling bi-quinary coded decimal, with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally used, but some allow simple fractional components (e.g. 1 ⁄ 2, 1 ⁄ 4, and 1 ⁄ 12 in Roman abacus ...
If each book had a mass of 100 grams, all of them would have a total mass of 10 93 kilograms. In comparison, Earth's mass is 5.97 × 10 24 kilograms, [5] the mass of the Milky Way galaxy is estimated at 1.8 × 10 42 kilograms, [6] and the total mass of all the stars in the observable universe is estimated at 2 × 10 52 kg. [7]
A form of unary notation called Church encoding is used to represent numbers within lambda calculus. Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the more likely the email is considered spam. 10: Bijective base-10: To avoid zero: 26: Bijective base-26
Tally marks represent one such system still in common use. The unary system is only useful for small numbers, although it plays an important role in theoretical computer science. Elias gamma coding, which is commonly used in data compression, expresses arbitrary-sized numbers by using unary to indicate the length of a binary numeral.
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These digits were used to represent larger numbers in the base 60 (sexagesimal) positional system. For example, 𒁹𒁹 𒌋𒌋𒁹𒁹𒁹 𒁹𒁹𒁹 would represent 2×60 2 +23×60+3 = 8583. A space was left to indicate a place without value, similar to the modern-day zero. Babylonians later devised a sign to represent this empty place.
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