[gweinberg]

Yeah, it may seem like a "better" (because stronger) conclusion to the author that if you have more pigeons than pigeonholes you must have more than one pigeon in a hole even if negative or irrational numbers of pigeons. But you're pretty much only invoking the pigeonhole principle in discrete math, where "more than one" means "at least 2".

[xg15]

Yeah, I think that was something that irked me about the "general" formulation: It suddenly brought in an average, i.e. a real, even though the "common" formulations only dealt with integers. This may be more general but made reasoning and understanding harder.