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Is it possible to write the number zero (0) in Roman numerals, and if so, how?

Question #62622. Asked by helenasykes. (Feb 17 06 6:35 AM)

mementoflash

And where is the sign for the Roman zero? There is none, because there is no need for zero.

http://www.mathematische-basteleien.de/romannumerals.htm

 Feb 17 06, 6:49 AM
Baloo55th

Roman numerals are not positional, so there is no actual need for a zero. In the system we use at present, we have 10 digits whose value at any time depends on the position they are in in the number - 1046 is quite different to 6401. In Roman numerals, MXXXXVI is the same as IXXXXMV. The first one is the usual way of writing it. However, in later times of Rome, a slightly positional system was used. MXXXXVI would be written MXLVI which can't be rearranged. Whichever way you write the Roman numbers, addition and subtraction are not too hard - you just collect like terms and count them up or cancel them out (making allowance for things like XL, of course. Division and multiplication are far harder. Decimals are impossible, and fractions difficult. Without the 0, a true positional system is not possible. You need to know that there aren't any hundreds in 1046. In the Roman system, you just didn't worry.

 Feb 17 06, 3:33 PM
helenasykes

Thanks, i realised the number 10 for example was X and didn't have a zero but i was curious as to what they would write if they had nothing, 5 minus 5 for example.

 Feb 18 06, 3:49 PM
Baloo55th

Oh, they had words for nothing - where we get nul from - but they didn't do calculations like we do. V take away V would be nullus (or something like that - not zero which only came much later as a word).

 Feb 18 06, 4:07 PM
davejacobs

I don't think it is quite right to say that Roman Numerals are not positional. IX (equivalent to decimal 9) is different from XI (equivalent to 11) for example.

 Feb 19 06, 11:50 AM
Baloo55th

If you refer to my posting of Feb 17th, you'll see I covered that. IX for 9 is later Roman usage. In the early days, IX and XI would have made no difference. It is not positional in the mathematical sense, though. Positional means that in a number ABCD a 2 in the A column is 2000 not 2; in the B column it's 200, and so on. A Roman I is a 1 wherever it is. A V is a five, never 500. You can't do addition of Roman numbers by writing them like this:
234+
163
---
397
That's what Positional means (and to see that properly, you'll have to click on the question - in Recent Replies it'll be all on one line and look silly).
IX is just a shorthand to save carving so many letters. It's not a mathematical feature.

 Feb 19 06, 12:08 PM
davejacobs

My apologies, Baloo55th, I jumped in with both feet before reading all your posting. Sorry!
I totally agree with your definition of positional. What I really meant was that in later Roman number symbology, the position of a symbol does matter. I think you can say that in general if a smaller number precedes a bigger one, it takes a negative value rather than a postive one.

There was a TV program recently where a professor of mathematics and a schoolgirl with a slate did the same multiplication, I think of a four digit number by a two digit one. He was given the two values in Roman representation, and had a bunch of spare symbols beside him: she was given the values in modern positionsl decimal form.
The girl finished in half the time he took. Sadly TVs usual dumbing down meant that the method he used was not fully explained, but it looked as though he was doing successive additions of each Roman numeral, etc.
What is plain though is that there had to be some way for engineers to do the calculations necessary for building those aqueducts, and for merchants to calculate the relative prices of things and their profit and loss accounts. However clumsy, they must have had some way of doing it.
Cheers, DaveJ

 Feb 19 06, 1:39 PM
Baloo55th

Oh, yes, there were quicker ways than the laborious written method.

http://www.bookrags.com/sciences/mathematics/abacus-mmat-01.html

http://www.ee.ryerson.ca:8080/~elf/abacus/roman-hand-abacus.html

 Feb 19 06, 2:47 PM

 How do you write zero in Roman numerals?

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