#RomanNumerals #Limitation #NumericSystem #Counting #Mathematics
Have you ever wondered why Roman numerals can’t go beyond 3,999,999? Let’s delve into the fascinating world of Roman numerals to unravel this mystery! ๐ง
## The Roman Numeric System ๐บ
Roman numerals are a numeric system that originated in ancient Rome and were used extensively in various aspects of daily life, from numbering years on buildings to counting the population. This system comprises seven basic symbols: I (1), V (5), X (10), L (50), C (100), D (500), and M (1000).
## The Limitation of Roman Numerals ๐
The Roman numeric system has a limitation in representing large numbers efficiently. As the symbols are based on addition and subtraction, the representation becomes increasingly complex as the numbers get larger. This complexity makes it impractical to go beyond a certain point, which in this case is 3,999,999.
## Why 3,999,999? ๐ค
The largest number that can be expressed in Roman numerals using the standard symbols is MMMCMXCIX, which represents 3,999. To go beyond this number, an overline or vinculum is placed above the numerals to indicate multiplication by 1,000. However, this method becomes unwieldy and non-standard beyond a certain point, leading to the limitation of 3,999,999 in practical use.
## Real-Life Examples ๐
Imagine trying to represent a number like 5 million in Roman numerals. It would require a cumbersome combination of symbols and overlines that are not commonly used or recognized. This difficulty in readability and standardization is why the Roman numeric system is typically limited to smaller numbers in practice.
## In Conclusion ๐
While Roman numerals have a rich history and cultural significance, their practical limitation in representing large numbers is a result of the system’s inherent complexity. For everyday use and numerical operations beyond 3,999,999, modern numeric systems like the Arabic numeral system are more efficient and accurate.
So next time you encounter a number beyond 3,999,999, you can appreciate the simplicity and convenience of our modern numeric system! ๐ก
Remember, while Roman numerals have their charm and historical importance, their practical limitations make them unsuitable for representing extremely large numbers in a clear and concise manner.
Because any time the number 4 or 9 is used its represented as 1 place values less than 5, for instance 4 is IV with the I infront indicating the number is 1 less than V(5) or XL meaning X(10) less than L(50) so for 4,000,000 you’d need a number for 5,000,000 which does not exist in traditional numerals. Meaning the largest you can go in the millions place is three million before you either cannot or have to break standard.ย
Roman numerals were composed using the following symbols:
* I = 1
* V = 5
* X = 10
* L = 50
* C = 100
* D = 500
* M = 1,000
As you probably know to denote values other than those you combined them. II for two, XXVIII for twenty eight, etc.
In order to denote larger numbers there was a mark known as a vinculum which was a solid line written above a number which indicated you should multiple it by 1000. So to get 1 million (1,000 * 1,000) you would write Mฬ (M with a line above it). Mฬ Mฬ Mฬ (imagine the line is solid and connected) would be 3 million. (MMM being 3,000).
3,999 = MMMCMXCIX
3,999,000 = Mฬ Mฬ Mฬ Cฬ Mฬ Xฬ Cฬ IXฬ
999 = CMXCIX
3,999,999 = Mฬ Mฬ Mฬ Cฬ Mฬ Xฬ Cฬ IXฬ CMXCIX
So that’s the limit right? Well technically no, there was another notation, called box vinculum which would be written as a 3 sided box over the number to be multiplied by 100,000. That means you could write |Mฬ | to mean 1,000 * 100,000 or 100,000,000. And thus |Mฬ Mฬ Mฬ Cฬ Mฬ Xฬ Cฬ IXฬ | would be 399,900,000 so 399,999,999 would be the largest number you could write using the notation system. |Mฬ Mฬ Mฬ Cฬ Mฬ Xฬ Cฬ IXฬ |Xฬ Cฬ IXฬ CMXCIX
It can, and there are several ways.
The Roman numeral system is additive. M = 1000; MM = 2000. So if you write enough Ms, you can theoretically write a number as high as you want. Write 5000 Ms in a row, you’ll be up to 5 million.
But that’s impractical, and so it was also non-standard. You don’t usually write more than three, at most four of any single symbol in a row. To get to higher numbers, the Romans and later Medieval scribes [developed different ways](https://en.wikipedia.org/wiki/Roman_numerals#Large_numbers) of writing:
* CIโ = 1000, and then the short form of CIโ was โ. But then Romans would write a pair of arcs, C and โ, around an I. This way of writing 1000 actually dates back to the Etruscans before them. Each extra pair of C and โ would raise the value by another power of 10, so:
* CCIโโ = 10,000 (short form โ)
* CCCIโโโ = 100,000 (short form โ)
* The Romans never actually wrote longer versions, but a theoretical CCCCCIโโโโโ would be 10,000,000.
* The [*vinculum*](https://en.wikipedia.org/wiki/Roman_numerals#Vinculum), a line drawn over the figure.
* If the Romans drew a line over a figure, that meant it would be multiplied by a thousand. So Xฬ Xฬ Xฬ Iฬ Iฬ would be equal to 32,000. Although “M” for 1000 did not actually develop until the middle ages, Mฬ Mฬ Mฬ Mฬ would be an acceptable roman numeral way to write “4,000,000”.
* Additionally, any figure inside of a three-sided box was multiplied by 100,000. Using that notation, |Xฬ | would be another way to write a million, while |Mฬ | would be a single symbol that would indicate a hundred million.
Mixing and matching these conventions (which are authentic, centuries old, I’m not making them up at all) makes it relatively easy to write up to around 399,999,999, which would be |Mฬ Mฬ Mฬ Cฬ Mฬ Xฬ Cฬ | Cฬ Mฬ Xฬ Cฬ Iฬ Xฬ CMXCIX, even without going the fully-non-standard route of just piling on Ms, and also without making up any new notations.
However, what’s true is that the limits of Roman numerals as they were actually used, starts to become apparent at this point; any higher, and you start having to rely on writing out four symbols in a row, or combining the system’s parts in ways that were never done historically.
The reason why the Roman numeral system was never extended any farther than this, is because neither the Romans nor medieval scribes ever needed to talk about larger numbers that we take for granted today: a billion, a trillion. If users of Roman numerals *had* ever needed to speak about much larger numbers, they might’ve started combining โ and โ with the *vinculum*. The current global population of 8,103,263,100 people might’ve been written something like this, for example: |โฬ โฬ โฬ โฬ Mฬ Xฬ Xฬ Xฬ | Cฬ Cฬ Lฬ Xฬ Iฬ Iฬ Iฬ C
I donโt know who told you that Roman numerals canโt go beyond 4 million, but itโs not true. (Iโm an anthropologist who studied Ancient Rome quite a bit)
There are several records from Ancient Rome that record millions and millions of sestertius, e.g. tax revenue, salaries for the army, sacks of grain from Egypt, tariffs from trade. Etc.
1 billion is simply an ((M)) usually written as an M with two strokes above (called vinculum).
And a note regarding some other comments: I see many โrulesโ regarding Roman numerals. However many of these supposed rules where actually postulated by mathematicians in the renaissance. So well over 1000 years after the fall of the western Roman Empire. These guys were really bored nerds and didnโt want to accept that classical antiquity wasnโt perfect, so they made up a โperfectโ mathematical system. These are also the guys who thought ancient statues and temples were not painted and were always white. They were wrong about a lot of things. (There are people like this today, who think classical antiquity was all white – if you catch my drift.)
Classical Romans (so between 500BC-500ADish) were not even remotely as strict with mathematical rules as some people think! Some wrote 4 as IV. Some wrote 4 as IIII. You can spot 99 written as IC or as LXXXXVIIII. Famously on the colosseum is a gate XLIIII (44), while just a few hundred meters away near the forum you can find a XXXXIV (44), both from a similar time period.
They also got quite creative. Mฬ is million. So you could see stuff like IV ~ Mฬ for 4 million. Or IIII โข Mฬ . Or Mฬ Mฬ Mฬ Mฬ .
So itโs absolutely possible to write 4 million. No one is gonna stop you, especially not a classical Roman.
Not an answer to your question but at the same time there’s no Roman numeral for zero either
>Eli5 why canโt Roman numerals go beyond 3,999,999
Roman numerals are essentially a tally system, a counting system for buying and selling goods. There was no need to tally up that many objects, so the Romans didn’t feel the need to expand the system beyond that.
Other comments have technically explained the reason why it’s specifically 3,999,999.
I want to focus on the fact that even if the Romans invented new symbols, there would still be a (higher) limit for the numbers that could be represented.
Let’s say that the Roman emperor decided that the letter Z is worth 4 million, then the highest number would be 15,999,999, but it would still be finite.
A positional numeral system, such as the Arabic numerals that we use, allows you to not have any restriction, and provided that you have enough paper you could technically write any finite number with only the symbols 0123456789.
This is because, for example, the symbol “2” can mean two, twenty, two hundred, two thousand, etc… depending on WHERE it is. So to write a bigger number you just need to move to the left, and not to invent a new symbol.