[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.
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.