Is integer a commonly understood term?
Is it common for an English speaking person to understand the word "integer" (i.e. the whole numbers ..., -2, -1, 0, 1, 2, ...)?
Or should I not use that word outside the domain of mathematics or computer science.
I don't think you can assume integer is a term known outside the mathematics and computer science communities. Would my mother know what an integer is? No. I would use "whole number" to describe it, which I believe is better understood.
If you look at ngram search between 1900 and 2000 of words integer, rose and fun:
you will find integer least common, but still referenced >1M times and yes vast majority of the books will be from mathematic and computer science, but I would say that such a concept that is thought in primary school falls under general knowledge and is common.
EDIT: While checking some of smackfu findings I stumbled over the article where an author has no problem in admitting that integer is not in his general knowledge. So, maybe I jumped to conclusion that it is really common.
On the other hand - searching New York Times find ~160 posts and articles using the word (here are the results for integer, it does not include results for integers).
Education is very much widespread today, and Mathematics are an integral part of this education.
The idea of "integers" would therefore be quite well known, and generally understood.
My normal test is whether a large daily newspaper will use the term without giving a definition on first use. Looking back through archives will also tell you if a word has become accepted as commonly known over time. Unfortunately a newspaper will almost never have the need to use "integer" or synonyms, and I only found one decent cite in the NYTimes archive from 1981: "This has to do with determining how many ways a whole number, or integer, can be written as a sum."
On the other hand, you could also use the same lack of results to argue that a newspaper will never use the word integer outside of a math context.