Base of Roman/Greek numbers?

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SO I had this discussion with a friend, and I thought that the Romans had a base7 system, as they have only 7 numerical symbols. And the Greeks have 27, so base27

Now this is incorrect, but I'm not sure why.
Can anyone explain?
 

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  • #2
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SO I had this discussion with a friend, and I thought that the Romans had a base7 system, as they have only 7 numerical symbols. And the Greeks have 27, so base27

Now this is incorrect, but I'm not sure why.
Can anyone explain?
I don't recall how the Greek numbering system went, but the system the Romans used was not base-7 or any other system that uses place values. In a system that uses place values, each digit represents multiplication of that digit by the base to some power.

Roman numerals didn't use places, but instead were similar to "tally" counting systems. IOW, systems that use one mark for each thing counted. To make it easier to keep track of large numbers, after four things are counted, a diagonal line through the four tally marks indicates a count of five. So instead of laboriously counting each mark, you can save some time by counting by fives.

The Roman system was similar. Instead of counting five things like so - IIIII - they used the letter V, which is supposed to symbolize a human hand with its five fingers. For ten they used X, which I believe is supposed to represent two hands, or ten fingers (possibly the X is a V on top of an upside-down V). I'm not sure what the origin of L is, but C (for 100) came from centum, and M (for 1000) came from mille.
 
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AlephZero
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The Greek system is base 10.

The basic idea was to use the letters of the alphabet to represent the digits. An "english" version of it would be
A = 1, B = 2, C = 3 ... I = 9
J = 10 K = 20 L = 30 ... R = 90
S = 100 T = 200 etc

So for example the number 234 was written as TLD, and 301 as UA. A special sign meaning "this is a number" was added, if the letters might be confused with a 2 or 3 letter word in a sentence.

Not all of the 27 different symbols have survived as letters in the modern greek alphabet.

The full Greek system could represent integers larger than 999 - in fact it could represent integers much larger than were of any practical use.

Unlike the Greeks, the Romans were not very interested in math and science apart from practical engineering, and the Roman system can't represent numbers bigger than a few thousand.

Nether the Greeks nor the Romans thought that "zero" was a number, so there was no symbol for it in either system, nor did they have any concept or notation for negative numbers.

The Greek and Roman systems were not used for actual calculation. That was done on an abacus, or an equivalent system of making marks on a surface covered with sand, which could quickly be "erased" to start a new calculation.
 
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