# On the usage of words instead of numbers to denote numbers

[To the best of my knowledge, I did not find any previous question that deals with this issue. I hope it is not a duplicate.]

I have a problem with the way in which mathematicians sometime use words instead of numbers to actually denote numbers. To me it seems that numbers should always be used whenever we are actually talking about numbers, however it is not really the case.

EXAMPLES:
1) "Probability one" or "Probability 1"?
2) "Measure zero" or "Measure 0"?
3) "Solution larger than one" or "Solution larger than 1"?
4) "The value is one" or "the value is 1"?

In all these cases, I think the proper way of writing is the second one, however I often find the first way.

To me this looks particularly incoherent, because the same authors shamelessly move to the second style whenever the number is slightly awkward (i.e. it is not an integer). Indeed, it is quite easy to find somebody who writes down "probability one", and then later on writes "the value is $1/2$". [Please, note that I am not referring to a sentence like "the value of $\alpha$ is $1/2$", that can be easily rephrased in a more readable expression such as "where $\alpha = 1/2$".]

Here there are my questions.
1) Is there a general rule to write down numbers?
2) Is my intuition correct about the way in which things are usually written?
3) Is my intuition correct about the way in which things should be (on logical and grammatical grounds) written?

Thank you in advance for any feedback!

PS: True enough, the first and the second examples can be considered slightly different from the third and the fourth, because - even if it actually applies what I claim (i.e. writers use words to denote numbers) - those could be considered expressions that have developed historically an inner meaning that goes beyond the fact that they indirectly refer to numbers.

• Be glad we are not required to say "unity", as mathematicians used to do when writing the number $1$ as a word. Aug 26, 2014 at 14:25
• In german I learned that only the integers $0,...,12$ should be written out as words, everything else should be written as number. But this is rather a general rule, an does even in german not necessarly apply to mathematical texts. Aug 26, 2014 at 14:25
• I think this has less to do about mathematics and more to do about writing style. When I was going through elementary and secondary school, the rule of thumb was to use words for numerals less than 10, and to use the numerals for 10 and up. Aug 26, 2014 at 14:25
• @Hayden (and flawr): Yes, non-mathematical writing has general rules like this. Kolmin says it is illogical for mathematical writing. I say to Kolmin: go ahead and to it your way, but don't complain when others do it in other ways, Aug 26, 2014 at 14:28
• @GEdgar: I see what you meant. Thus my question is, which one of the two forms I presented do you consider good mathematical writing? (More or less in the same way in which there is bad mathematical writing for Serre). Aug 26, 2014 at 14:31

• @Kolmin Further, natural language may inhibit intrinsic mathematical pattern matching. For a simple example, compare: "in a domain, $\, x^{\color{#c00}{\large 5}}-a\,$ has at most $\,\color{#c00}5\,$ roots", vs. "five roots". Using precisely the same symbol $\,\color{#c00}5\,$ in both places helps the reader to see the relationship between the degree and the number of roots. In less trivial examples, such pattern-matching can be greatly obfuscated by the use of natural language. Aug 26, 2014 at 15:18