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Name:  unterman
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Question:
If such a thing exists, what is the largest number that can be represented by Roman Numerals?



Replies:
Okay, I'll have a shot at theis question and someone should correct me if I'm wrong. If I'm remembering my Roman numerals properly, the following equivalences hold:

I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

I can't remember any other numerals. As well, I thought that a numeral with a bar over it stood for 10 times the value of the numeral without the bar. (Actually this must only be the case for M and D since it would be pointless for any other numeral) Thus, the number 10,000 could be easily made with:
_
M

So, for a single digit, this would be my guess as the largest number that could be made. How many overscored M's could one string together? I have no idea. If we accept that no more than 3 could be (as none of the other numerals can be put together with more than 2 others of the same type), then we get:

___
IMMM

which comes to 39999 in out decimal system.

-Christian


I'm not sure how I managed that, but 39999 is clearly not

___
IMMM in Roman numerals.

So, in revising my answer (I really should have reiviewed that message before posting it), I believe that

___ _
MMMXMVIII = 39998

is the largest as one more would be 39999 which would be

_____
IMMMM which has four overscored M's in a row. I hope that answer holds up better than my last one!

-Christian


I have read a bit more and had a few discussions about this Roman numeral question and I think I should revise my answer. First of all, an overscored M stands for 1 000 000 or one thousand times its normal value. This changes things a bit!

As well, there is some debate as to whether numbers such as 9 should be written as IX or VIV. It seems that some books say one thing and other books say different things. My dictionary implies that subtractions can only be made from numerals that are immediately larger. Thus, 99 is written as LXLVIV and not as IC.

However, nowhere could I find any reference to a maximum numeral. Perhaps there is some rule about how many symbols can be used, but I have not found it. Thus, it would be legal (taking the liberty of assuming that anything not illegal is legal) to write as many overscored M's as one wishes and make a number as large as one wishes. I suspect that the Romans did not have much use for numbers greater than a few million and thus this problem seldom came up. It is not unlike asking what is the largest number that can be written with English words (and not Arabic numbers). There are words for really big numbers like a dectillion (I think that is the word) and a google and a googleplex. However, people seldom use them and so no one worries that they won't be able to write out a check properly because there aren't any words for the number they wish to make the check out for!

-Christian



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