5 ms·
A terminology note, I think "first category"/"second category"/"residual" have largely been replaced by the clearer "meagre"/"non-meagre"/"comeagre". Or at lea
by Sniffnoy 8y ago
A terminology note, I think "first category"/"second category"/"residual" have largely been replaced by the clearer "meagre"/"non-meagre"/"comeagre". Or at least, I hope they've largely been so replaced, because geez the old terminology is a pain. :P
- mcguire 8y agoClearer?!?
- antidesitter 8y agoI'd say so. "non-meagre" = not meagre = positive, and "comeager" = complement of meagre = full. The only thing you have to remember is what "meagre" means.
- Sniffnoy 8y agoYes. "Meagre" means small. Which is what a first-category set is, but the name "first category" doesn't tell you that (how is one supposed to remember which of first and second category is which?). And then after that, you don't need to introduce any more words. If you mean to say something is not meagre, you just say it's not meagre, same as you would with any concept. If you mean to say it's complement is meagre, you just say it's comeagre, same as with anything. The names "first category" and "second category" tell you nothing, not even making it obvious which is which -- and moreover, they make it sound like the two are both equally useful sides of a distinction, like finite and infinite, while in reality one of these is actually directly useful and the other is just everything that isn't that (which is how most distinctions in mathematics go; you wouldn't make up a separate new word for "not compact", for instance). And then "residual" makes it sound like there's some new thing going on, when of course it's really just being co-first-category. But co-first-category's quite the mouthful, isn't it...?