In Japanese, a 文【ぶん】 is basically anything which is delimited by periods (マル) or question/exclamation marks. For example, let's say there is a paragraph like this in the middle of the main text of a novel.
Here, we have rather simple 体言止め expressions, which make this paragraph compact yet dramatic. Despite being 体言止め, I believe there are three 文 in this paragraph, simply because there are three periods. If I were to explain this paragraph with grammatical terms, I would say something like this: "This is a paragraph which contains three sentences. Each sentence lacks a main predicate; instead, one long noun phrase forms the entire sentence."
However, on this site, I keep seeing assertions like "Strictly/Grammatically speaking, this is not a sentence in the first place" to explain this pattern. And to my surprise, apparently many users favor this type of explanation. The most recent example is this.
So I thought, "Ah okay, grammatically speaking, sentence in English means something different from 文 in Japanese, and a sentence always needs a main predicate!"
However, I failed to find any credible source to support this. All the serious English articles I've read so far say that a sentence doesn't necessarily have a main predicate. For example, "Hi.", "Yes.", "At three o'clock." and "Two pizzas with cheese crust, please." are English sentences (categorized as minor sentences) simply because they begin with a capital letter and end with a period. Simply put, I found essentially no difference between sentence in English and 文 in Japanese.
So my question is as follows: Is 文 different from sentence? Ordinary English speakers have an idea of sentence which is different from the formal dictionary definition? English speakers who are learning Japanese actually tend to feel there is no sentence in the paragraph above? If yes, how many sentences are there in this article? I feel there are dozens of 文's, and I have never doubted that. On a website where not everyone is an expert, is it unsafe/misleading/unpractical to call the 文 above 'Japanese sentences'?
As far as I can tell, I have never seen a Japanese article which says something like "体言止めの"文"には述語がないので、厳密な文法的には文ではありません".