Why were the Greek and Roman systems of numbers not used for actual calculation?

In summary, the Roman system used only 7 symbols while the Greek system used 27. The English version of the Greek system would be A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26. The Roman system used V for 10, X for 20, L for 30, M for
  • #1
Synetos
40
1
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
Synetos said:
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.
 
  • #3
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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1. What is the base of Roman and Greek numbers?

The base of Roman and Greek numbers is a system of counting and writing numbers using letters rather than digits. Both systems use a base of 10, which means that there are ten different symbols used for counting: I, V, X, L, C, D, and M in Roman numerals, and Ι, β, γ, δ, ε, ϛ, ζ, η, θ, ι, ια, κ, λ, μ, ν, ξ, ο, π, ϙ, ρ, σ, τ, υ, φ, χ, ψ, and ω in Greek numerals.

2. How do I convert Roman and Greek numbers to our modern number system?

To convert Roman and Greek numbers to our modern number system, you can use a conversion chart or calculator. Each letter in the Roman or Greek number represents a specific value, and you simply add or subtract these values to get the total number. For example, the Roman number IV is equal to 4 (1+5=4) and the Greek number ια is equal to 11 (10+1=11).

3. How were Roman and Greek numbers used in ancient times?

Roman and Greek numbers were primarily used for counting and recording the amount of currency, livestock, and other goods. They were also used for dating and marking the years in calendars. These numbers were widely used in the ancient Mediterranean world and were an essential part of daily life.

4. Are there any limitations to using Roman and Greek numbers?

One limitation of using Roman and Greek numbers is their lack of a symbol for zero. This made it challenging to perform mathematical operations, such as multiplication and division. Additionally, the symbols used in these systems can be lengthy and complicated, making them less efficient for large numbers.

5. How did the Roman and Greek number systems develop?

The Roman number system is believed to have originated around 500 BC from the ancient Etruscan civilization. The Greek number system is thought to have developed from the Phoenician number system around the same time. Both systems evolved over time and were heavily influenced by other civilizations, such as the Egyptians and Babylonians.

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