It's often said that the axioms of ZFC set theory are the foundation of mathematics, but the same people who say that also use the term "class" a lot. For example, "the class of all ordinals", is apparently too large to qualify as a set. What's bugging me right now is that I read that there's no such thing as classes in ZFC. There's nothing but sets. So why are people using the term "class" at all? I guess the answer is "because it's useful". But shouldn't we either refrain from using that term, or say that we're actually using NBG, not ZFC.