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In primary school I learned that numbers less than 13 should be spelled out in writing.

I am suddenly not sure anymore, how I should handle this situation when it comes to article writing in mathematics.

What is better in the context of a Theorem?

Given five sets $X_1, \ldots, X_5$

or

Given $5$ sets $X_1, \ldots, X_5$

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9  
I personally would write "Given five sets ... ", but "Because $5$ is a prime ..." (just to give 2 examples of different usage). –  Hagen von Eitzen Nov 20 '12 at 20:05
9  
you mean "two examples" :-) –  andy Nov 20 '12 at 20:07
3  
To elaborate on Hagen's remark (with which I agree), I tend to write out small numbers when they are used to enumerate some objects (e.g. "five sets"). I only write numerals to refer to numbers as objects in their own right (e.g. "5 is a prime"). –  Austin Mohr Nov 20 '12 at 20:11
    
Also, for what it's worth, I write out numbers up to ninety-nine in words. I also write out even denominations like "five million", since I see this as enumerating the number of millions (five of them). –  Austin Mohr Nov 20 '12 at 20:17
5  
Obviously it should be "Given five sets $X_{\text{one}}, \ldots, X_{\text{five}}$". :) –  Rahul Nov 20 '12 at 20:28
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closed as off topic by Will Hunting, Austin Mohr, yunone, N. S., J. M. Nov 22 '12 at 8:41

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1 Answer

up vote 1 down vote accepted

http://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers

Some of the points in the excerpt below might be regarded as being within the competence of mathematicians-qua-mathematicians: "Sometimes figures and words may carry different meanings, for example Every number except one implies that there is one exception (we don't know which), while Every number except 1 means that the specific number 1 is the exception.", "Numbers in mathematical formulae are never spelled out (3 < π < 22/7, not three < π < 22 sevenths).",

begin excerpt

As a general rule, in the body of an article, single-digit whole numbers from zero to nine are spelled out in words; numbers greater than nine, if they are expressed in one or two words, may be rendered in numerals or in words (16 or sixteen, 84 or eighty-four, 200 or two hundred); those requiring more than two words are given in numerals (3.75, 544, 21 million). This applies to both ordinal and cardinal numbers. However there are frequent exceptions to these rules.

  • In tables and infoboxes, quantitative data is expressed as numerals; numerals will also fit better in limited space. Numbers within a table's explanatory text and comments should be consistent with the general rule.
  • Comparable quantities should be all spelled out or all figures: we may write either 5 cats and 32 dogs or five cats and thirty-two dogs, not five cats and 32 dogs. Adjacent quantities which are not comparable should usually be in different formats: twelve 90-minute volumes or 12 ninety-minute volumes is more readable than 12 90-minute volumes or twelve ninety-minute volumes.
  • Numbers that begin a sentence are spelled out, since using figures risks the period being read as a decimal point or abbreviation mark; it is often better to recast the sentence than to simply change format, which may produce other problems; e.g. do not use Nineteen forty five and 1950 were important elections for the Labour Party, but rather The elections of 1945 and 1950 were important for the Labour Party.
  • The numerical elements of dates and times are not normally spelled out (that is, do not use the seventh of January or twelve forty-five p.m. or Two thousand eight was the year that ... ). However, they should be spelled out where customary in historical references such as Seventh of March Speech and Fifth of November; these are treated as proper names.
  • Centuries are given in figures or words using adjectival hyphenation where appropriate: the 5th century BCE; nineteenth-century painting. Neither the ordinal nor the word "century" should be capitalised.
  • Common fractions for which the numerator and denominator can be expressed in one word are usually spelled out, e.g. a two-thirds majority; use figures if they occur with an abbreviated unit, e.g. 1⁄4 yd and not a quarter of a yd.
  • Mixed fractions are usually expressed in figures, e.g. 2 1⁄4; however, the fractional part should always be consistent with the integral part, e.g. Nine and a half, and not Nine and 1⁄2
  • Percentages are usually written with figures, e.g. 10 percent or 10%.
  • Numbers in mathematical formulae are never spelled out (3 < π < 22/7, not three < π < 22 sevenths).
  • Do not use spelled-out numbers before symbols for units of measurement: write five minutes, 5 minutes, or 5 min, but not five min.
  • Measurements, stock prices, and other quasi-continuous quantities are normally stated in figures, even when the value is a small positive integer: 9 mm, The option price fell to 5 within three hours after the announcement.
  • When expressing large approximate quantities, it is preferable to write them spelled out, or partly in figures and part as a spelled‑out named number; e.g. one hundred thousand troops may be preferable to 100,000 troops when the size of the force is not known exactly; write Japan has the world's tenth largest population, with about 128 million people (as it is just an approximation to a number likely to be anywhere between 127,500,000 and 128,500,000), but The movie grossed $28,106,731 on its opening day (the exact quantity).
  • Sometimes, the variety of English used in an article may call for the use of a numbering system other than the Western thousands-based system. For example, the South Asian numbering system is conventionally used in South Asian English. In those situations, link the first spelled-out instance of each quantity (e.g. [[crore]], which yields crore). (If no instances are spelled out, provide a note after the first instance directing the reader to the article about the numbering system.) Also, provide a conversion to Western numbers for the first instance of each quantity, and provide conversions for subsequent instances if they do not overwhelm the content of the article. For example, write three crore (thirty million). Similarly, if you write 3,00,00,000, also write (30,000,000) or (30000000). (Note that the variety of English does not uniquely determine the method of numbering in an article. Other considerations, such as conventions used in mathematics, science and engineering, may also apply, and the choice and order of formats and conversions is a matter of editorial discretion and consensus.)
  • When both a figure and spelled-out named number are used in a quantity, it is useful to use a non-breaking space, as in 128 million or 128{{nbsp}}million to prevent a line break from occurring between them.
  • Sometimes figures and words may carry different meanings, for example Every number except one implies that there is one exception (we don't know which), while Every number except 1 means that the specific number 1 is the exception.
  • Proper names, formal numerical designations, and other idioms comply with common usage; e.g. write Chanel No. 5, 4 Main Street, 1-Naphthylamine, Channel 6, Fourth Amendment, Seventeenth Judicial District, Seven Years' War. This is the case even where it causes a numeral to open a sentence, although this is usually avoided by rewording.

end of excerpt

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