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In the hebrew bible, there number system is based off of hebrew letters. There is a single digit used going all the way up to 10, then it uses two digits... Untill it gets to 20, which is a single digit again. The actual hebrew numbers go in sequence of: 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60, 70, 80, 90, 100, 200, 300, 400. What base of numbers would that be+

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Thanks to indians who found the decimal base and arabs who brought it to europe.. we could make a difference between pure prose and literature and arithmetics :) –  El Moro Apr 29 '11 at 19:36
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Actually the Hebrew Bible does not use this notation. All numbers there are written out in words. –  Robert Israel Apr 29 '11 at 23:14

5 Answers 5

up vote 13 down vote accepted

Actually, the values of the letters continue up to 90, then 100, 200, 300, and finally 400 for the tav (see the Wikipedia page on Gematria). (The values for the "terminal letters", like the nun-sofit, are, I believe, more "recent").

But this is not a base system, because the system is not positional, it is aggregate: the value of a latter/symbol does not depend on its position, the way it does in decimal, binary, etc., but only on the letter. So two words that are made up of exactly the same letters, though perhaps in different order, would correspond to the same value. This is not true of positional/base systems.

It's even worse than the Roman numerical system, because there are no positional rules here the way you have for Roman numerals.

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How would you describe the difference between regular Hebrew gematria and a new system where the letters in the abjad take on in ascending order values equivalent to those numbers containing exactly one non-zero digit in some base aside from 10? –  Double AA May 20 '13 at 1:03
    
(To clarify, the system to compare to would be (in "base" 5): א1 ב2 ג3 ד4 ה5 ו10 ז15 ח20...מ45 נ50 ס100 ע150...ש400 ת450) –  Double AA Aug 14 at 16:53

The hebrew numerals don't have a base, because they're not a positional numeral system any more than Roman numerals are.

(There are some usages that reuse letters for values 1000 times as big. In that sense, it is base 1000, but that's stretching definitions a bit.)

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Hebrew is an interesting number system that isn't in a base like ours is. Here is a link to wikipedia's article on the Hebrew numbers - the idea is that they just came up with new symbol for bigger numbers, like the Roman Numerals or Etruscan Numerals did.

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The Hebrew numerals constitute a decimal system, however it's different from the Arabic decimal system in that the symbols do not recycle through all the orders of 10^n. So a symbol's position in a string does not impact the symbol's value. Because of this, the system, does not scale elegantly. It's not really used for doing math (generally) nor representing very large numbers (though they could be if a system of infinite extension were devised). Let vector A = [1,2,3,4,5,6,7,8,9], then, left to right, the numerals B = [ט,ח,ז,ו,ה,ד,ג,ב,א] are (10^0)A respectively; and are the only symbols ever in the 10^0 place . Numerals C = [צ,פ,ע,ס,נ,מ,ל,כ,י] correspond to (10^1)A, and D = [ץ,ף,ן,ם,ך,ת,ש,ר,ק] (alternatively, D = [תתק,תת,תש,תר,תק,ת,ש,ר,ק]) to (10^2)A. These basic symbols have been extended somewhat with apostrophes and dots, but is still quite limited in the range of represented values. Zeroes do not need a symbol in this system, because it is not dependent on position. If you were using Hebrew numerals as a tool for calculation, cognizance of the decimal exponent would need to be taken, as well as how the elements of B, C, and D scale from one vector to another through the various operations.

So, that was the symbols, but base 10 clearly shows up in the naming convention, too. Names for ones, tens, hundreds, and thousands. They cycle just as regularly as you would expect. The naming does get a little strange, though, with names like shesh me'ot elef usheloshet alafim vachamesh me'ot vachamishim, literally six hundreds of thousands and three thousands and five hundreds and fifty, for 603,550. They tended to split the number up, ordered in terms of hundreds, with higher orders said before lower orders, just as in English; but, within each order-group, hundreds will be said first, then ones, and then tens.

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Hebrew uses a decimal system, with heiratic tokens.

The decimal nature corresponds to that there are symbols for 1, 10, 100, etc.

The heiratic nature corresponds to using separate symbols for 1, 2, 3, 4, 5, ..., 9 in each place. This was the style of the heiratic system in Egypt, and used in alphabetic systems throughout the ancient world.

The modern form might be seen in a series of stamps for 1c, 2c, ... 9c, then 10c, 20c, 30c, .. 90c, and then £1, £2, ..., £9, ... etc, as formerly used on railway small freight. One makes up £1.63 with a £1 stamp, a 60c and a 3c stamp.

Of course, one notes that the choice of letter implies a notion of place, even if this is not so presented. Consider the abacus. This was the mainstay of calculation in ancient times, and ultimately the reference of numbers.

The western abacus consists of columns and rows, where the column value is the product of the row values. Carry depends on if there were a change of column.

The notation of the chinese and mayan is to attach a column weight and position, like saying 3c 2x 4i, meaning 3 in the hundreds, 2 in the tens, and 4 in the units.

Other notations use different ways of showing this. The tokens of the romans and kinderd folk, use the same scale we use of coins: each token means 1 or 5 in a specific column. So 2x is written as XX.

The alphabetic codes like the hebrew, greek and gothic, use a large number of symbols for "n in column C", the order of the alphabet provides a ready-made collection.

       D    L    V
  M    C    X    I

Since the notion of base and position rests in the abacus, and not the notation, it is fair to say that the base is decimal, and the selection from 7i vs 7x or 7c suggests that position was perfectly understood.

The modern notation derives from the greek alphabetic one, with 1x drafted to mean 0i. This is why, for example, 0 is after 9, rather than before 1. The use of the symbols for the i column, and a later substition of say 3i 2i as 3x 2i is an unfolding of the results.

Place was understood: it is what makes a base a base. Position is a function of notation, and does not destroy the place values.

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This directly contradicts the other answers posted. Do you have any sources that back up your claim? –  Zev Chonoles May 16 '13 at 8:35
    
demotic simply means 'of the people'. The late egyptian style was to use a symbol meaning eg (70). In any case, the argument presented here is that there was a special symbol for '70' that did not need an attendent 0, which is exactly what all of the previous posts say, and the modern example of stamps suggest (that one can make 1.63 from a 1, a 0.6 and a 0.03 letter. –  wendy.krieger May 16 '13 at 9:16
    
@Zev demotic ought read 'heiratic', which do have special symbols in this style, see eg page 257 of Richard Gillings "Mathematics in the time of the Pharaohs" (Dover print) –  wendy.krieger May 16 '13 at 10:48
    
@ZevChonoles. prehaps you might explain the contradiction, rather than posting glib statements. –  wendy.krieger May 20 '13 at 0:53

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