Definition:Roman Numerals
Definition
The Roman numerals are:
\(\ds \mathrm I:\) | \(\)unus\(:\) | \(\ds 1\) | ||||||||||||
\(\ds \mathrm V:\) | \(\)quinque\(:\) | \(\ds 5\) | ||||||||||||
\(\ds \mathrm X:\) | \(\)decem\(:\) | \(\ds 10\) | ||||||||||||
\(\ds \mathrm L:\) | \(\)quinquaginta\(:\) | \(\ds 50\) | ||||||||||||
\(\ds \mathrm C:\) | \(\)centum\(:\) | \(\ds 100\) | ||||||||||||
\(\ds \mathrm D:\) | \(\)quingenti\(:\) | \(\ds 500\) | ||||||||||||
\(\ds \mathrm M:\) | \(\)mille\(:\) | \(\ds 1000\) |
To express other numbers than these, symbols are placed next to each other so as to cumulate: for example:
- $\text {II}$ means $2$
- $\text {CCXVI}$ means $216$.
For brevity in presentation, the technique is used of placing a smaller denomination in front of a larger one so as to subtract the former from the latter
For example:
- $\text {IV}$ means $4$
- $\text {XCIX}$ means $99$ (although $\text {IC}$ could be used, it is not).
Arithmetic using Roman numerals is cumbersome and pointless, although some sadistic and worthless grade-school arithmetic texts insist on setting such operations as exercises.
For doing arithmetic, abacism was the usual technique, originating in ancient times. It is still used in rural areas of, for example, the Asian steppes, where writing materials are not to be wasted and electronic aids are un-needed.
With the invention of the techniques offered by the so-called Arabic numerals in mediaeval times, an alternative method of doing arithmetic developed, called algorism.
Uses of Roman Numerals
The Roman numerals are used today solely for enumeration in certain traditional contexts:
- $(1): \quad$ The presentation of years in dates, especially embedded in the masonry of buildings to indicate its year of construction
- $(2): \quad$ In the context of the cartesian plane, Roman numerals are traditionally used to enumerate the quadrants
- $(3): \quad$ Enumerations of lists, particularly when sublists are required which (because of the presentational style selected by the author) need different styles of presentation, for example: "See section $1 \ \text{(a)} \ \text{(iii)}$".
- $(4): \quad$ In the field of statistics, the nomenclature of type $\text I$ errors and type $\text {II}$ errors
Also presented as
It is commonplace to present Roman numbers in lowercase: $\text {i, v, x, l, c, d, m}$.
Warning
Because of the similarity in shape between the letter $\text I$ and the number $1$, it is a common mistake to confuse them and use $1$ where $\text I$ should be used.
Consequently, hilariously clumsy-looking constructions can be found in published works (usually in pretentious artwork such as can often be found on the covers of contemporary musical product) such as $\text V 1 1 1$ for $\text {VIII}$.
Also see
- Results about Roman numerals can be found here.
Sources
- 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $1$: Numbers: Real Numbers: $1$
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): Chapter $1$: Complex Numbers: The Real Number System: $1$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $50$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $50$
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $3$: Notations and Numbers: Roman numerals
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): number systems
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): numeral
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $16$: Roman numerals