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I am working on a math problem where I need some help with the English to finish my solution.

I have an ambiguous sentence:

At least one student attended every lecture.

My attempt to disambiguate this sentence are the following two possible meanings for this sentence:

(1) There exists a student, who attended every lecture.

Here I am trying to make clear that there is at least one student who attended every possible lecture.

(2) For every lecture, there was a student present.

Here I am trying to make clear that for every lecture which was held, at least one student was in attendance.

Would these sentences be adequate for what I am trying to say? Do you have any better suggestions?

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    This is a common problem. Your opening can be read rather petulantly: "At least one student... " It sounds like, "At least one person came to my party." If you make it passive it doesn't suggest that tone: "Every lecture was attended by at least one student." Commented Nov 14, 2020 at 1:43

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(1) tells me that there is a student who attended every lecture. The use of “a ...” suggests “one and only one” or may just mean “any one of many”. Hence the ambiguity, which may only be resolved by logical argument or convention.

(2) is similar. “There was a student present” is open to ambiguity, depending too much on the logical abilities of the reader to resolve it.

Can I do any better? It’s not easy because so much depends on the readers’ thinking habits and on their logical training.

Let’s try “One or more students attended each lecture” and see what other site members think. I suggest that “one or more” overcomes the ambiguity that may be read in by “a”.

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