Or is it just non standard to go beyond that large of a number?
In: Mathematics
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 M̅ (M with a line above it). M̅M̅M̅ (imagine the line is solid and connected) would be 3 million. (MMM being 3,000).
3,999 = MMMCMXCIX
3,999,000 = M̅M̅M̅C̅M̅X̅C̅IX̅
999 = CMXCIX
3,999,999 = M̅M̅M̅C̅M̅X̅C̅IX̅CMXCIX
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 |M̅| to mean 1,000 * 100,000 or 100,000,000. And thus |M̅M̅M̅C̅M̅X̅C̅IX̅| would be 399,900,000 so 399,999,999 would be the largest number you could write using the notation system. |M̅M̅M̅C̅M̅X̅C̅IX̅|X̅C̅IX̅CMXCIX
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.
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:
* CIↃ = 1000, and then the short form of CIↃ was ↀ. But then Romans would write a pair of arcs, C and Ↄ, around an I. This way of writing 1000 actually dates back to the Etruscans before them. Each extra pair of C and Ↄ would raise the value by another power of 10, so:
* CCIↃↃ = 10,000 (short form ↂ)
* CCCIↃↃↃ = 100,000 (short form ↈ)
* The Romans never actually wrote longer versions, but a theoretical CCCCCIↃↃↃↃↃ 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 X̅X̅X̅I̅I̅ would be equal to 32,000. Although “M” for 1000 did not actually develop until the middle ages, M̅M̅M̅M̅ 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, |X̅| would be another way to write a million, while |M̅| 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 |M̅M̅M̅C̅M̅X̅C̅| C̅M̅X̅C̅I̅X̅ 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 ↂ and ↈ with the *vinculum*. The current global population of 8,103,263,100 people might’ve been written something like this, for example: |ↇ̅ↂ̅ↂ̅ↂ̅M̅X̅X̅X̅| C̅C̅L̅X̅I̅I̅I̅ C
I don’t know who told you that Roman numerals can’t go beyond 4 million, but it’s not true. (I’m 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 “rules” 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 didn’t want to accept that classical antiquity wasn’t perfect, so they made up a „perfect“ 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. M̅ is million. So you could see stuff like IV ~ M̅ for 4 million. Or IIII • M̅. Or M̅ M̅ M̅ M̅.
So it’s absolutely possible to write 4 million. No one is gonna stop you, especially not a classical Roman.
>Eli5 why can’t 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.
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