It is not preposterous to check many dictionaries to see how a professional logician or a sailor or anyone else is using a particular word. That particular website does scan many on-line dictionaries but in fact found that word in only about a dozen.
The word "denumerable" was used in a way that hints at being synonomous with "infinite" but what is indeed preposterous about a layman looking up a new word in a dictionary? How else does one learn a new word, and in this case a word seemed, at least to me, to be misused?
I accept your usage of the word but it surely does not conform to what appears to be the more commonplace understanding of the word. Many words have multiple meanings, some quite arcane. What would have been wrong with just having used the term "infinitaly many" or some such phrase in that discussion when you were indeed talking to laymen, not professional logicians??