Numbering system

A numbering system is a whole of rules of use of the signs, words or gestures making it possible to write, state or of mimer numbers. In their written form, the latter were born, at the same time as the writing, of the need for organizing harvests, the trade and the dating.

Systems of stating

Certain numbers profit exclusively from a simple name, like thousand French . In the contrary case, several principles make it possible to compose them.

the addition: seventeen French (10+7);
the multiplication : two hundred French (2×100);
the subtraction : eighteen says duodeviginti in traditional Latin (two-of-twenty, 20-2);
the division : a manner of saying fifty is to haunt-kant into Breton (half-hundred, 100/2);
the protraction (term introduced by Claude Hagège): thirty-five holhu Ca kal into yucatèque was said (cinq-dix two twenties, 15 2×20, either 15 worms 2×20 or 15 starting from the score preceding 2×20, or 15+20). In the expression of 35 (as in that of thirty) it is advisable to restore an implied relator (or erased) who was you (actually ti+u with Ti = rental “towards” and U = personal index of 3rd person “its” who, in this context, was used to derive the ordinal one since the cardinal; so that the expression of 35 must analyze itself as being " 15 towards the second vingtaine". For more details to see CAUTY, A., 2002, `Of specificities of Maya numerations précolombiennes', Memory of the Company of Linguistics of Paris, New Series, volume XII, Leuven (Belgium), Peters, p.121-147; or also CAUTY, A., 2002, `the protractif type of numerations of the Maya surface', Made Languages, n° 20: Mesoamerica, the Caribbean, Amazonia, vol. 1, Paris, Ophrys, p. 85-93.

An auxiliary system is sometimes used. Compared to the principal system, this one perhaps:

lower : numeration wolof is decimal but uses an auxiliary quinary system, twenty six says ñaar fukk ak juroom Ben in wolof (two ten and five one, 2×10+5+1);
higher : Basque numeration is decimal but uses an auxiliary vigesimal system, hundred fifty-two is said in ehunta berrogeita hamabi out of Basque (hundred-and two-twenty-and dix-deux, 100+2×20+10+2). In the same way, in French of France persist eighty and ninety (instead of Huitante in Switzerland and of Ninety in Switzerland and Belgium), which comes from the medieval vigesimal system, used in an auxiliary way with the decimal principal system of Latin origin.

Lastly, certain numbers profit from a construction independent of the base employed. Thus, a manner of saying, respectively, eighteen, forty-five and forty-nine, into Breton, are triwec' H (proof spirit, 3×6) or daounav (deux-neuf, 2×9), pemp VOR (five nine, 5×9) and seizh seizh (seven seven, 7×7). It goes without saying this last form does not come from a base seven, but from the value symbolic system of this number. (The three last quoted forms are hardly any more employed.)

Reading of the numbers

The use in the various languages for the numbers differs largely in the way of grouping the figures: it is thus current to group the figures by two in French to state the long numbers like the phone numbers, of registration, serial numbers, etc… When the grouping used is ambiguous in the verbal communication, that can sometimes produce ambiguities of communication (for example eight hundred and eight hundred could want to say 800.800 or 808.100 if the tone or the rate/rhythm is not marked to clearly separate the groups in the statement from a phone number for example, which is avoided with the numbering systems symbolic system; this is why the long numbers are quoted in French rather with groups of two digits without raising however all ambiguities as for example twenty eighty five which could mean 24 25 or 20 85 in French of France, difficulty which does not exist in Swiss French or the old vigesimal system is completely abandoned; this difficulty rises however while marking the pauses between each group, and while avoiding any pause in the middle of the number eighty oral French of France; for the writing, it is feature-of union which raises ambiguity by binding the words composing the same grouping of figures, but the notation symbolic system is definitely preferable for such numbers because simpler and nonambiguous.)

Systems of MIME

The people make use traditionally of the parts of their body to count. For a decimal or quinary account, the fingers are generally put at contribution. The Yukis, which employ an octal system use spaces between the fingers to count. The people chepang, which employ a duodecimal system, make use of the inch to count on the phalanges of the fingers. Many other processes still were employed.

Marking systems

One schematically distinguishes three families from marking systems.

the additive systems use symbols to represent certain numbers, the other numbers being obtained by juxtaposition of these symbols. The reader has then the responsibility of add the values with each symbol to find the value of the number. It is the Greek case of the numbering systems , Egyptian, gotic, or more simply of the unary Système. It is also the case with a subtractive alternative for the Roman numbering system .
the hybrid systems use symbols different for the powers from the base and the numbers lower than the base written in front of the symbol. The numbers are thus represented by addition of multiples of powers of the base. It is the case of the numbering systems Chinese and Japanese. One can notice that such a marking system comprises a strong analogy with the system of stating of the numbers in a majority of languages. (For example, in French, the number two thousand - huit-cents-dix-sept , is also formed by addition of multiples of powers of base 10: 2×10 ³ +8×10 ² +1×10 ¹ +7.)
the positional systems uses a symbol for each unit, the place of these symbols in the writing of the number indicating the weight which is affected for them (weight 1, weight N, weight N ²,… for a base N). It is the case of the numbering systems Maya and Babylonian, as well as the numbering systems Indian and Arab, which is at the origin of the modern Mathématiques, those making it possible from now on to simply write the numbers whatever is the base, using the zero positional.

See too

External bonds

Number bases: NUMBERS: curiosities, theory and uses.

Be-X-old: Сыстэмазьлічэньня

Zh-min-nan: Sò͘-jī

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