semantics - 'A / One / At least one student entered the room.' Are these the same? (truth-conditionally)


I just wonder if the two following sentences are truth-conditionally the same. Sentence 1 essentially means there existed a student who entered the room, and this situation includes two, three or more students entering the room. Hence, I believe these two sentences are truth-conditionally the same. Are they?




  1. A student entered the room.

  2. At least one student entered the room.



How about




  1. One student entered the room



I gather this is different, as sentence 3 only means one student, not more and not fewer?


Any and all insights would be welcome.




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