This question already has an answer here:
- How is an empty set truly “empty”? 6 answers
I skimmed over this question Is the empty set a subset of itself?, and I'm currently under the impression that it's a widespread belief that the empty set contains itself. But a contradiction seems to arise: if the empty set contains itself, then it's NOT empty. After all, if we call a set non-empty just because it contains the empty set, then why should we treat the empty set itself differently?
Then it occurred to me that maybe mathematicians define "empty" differently in set theory. Maybe by "empty set" they mean a "set that contains only itself", instead of a "set that contains absolutely nothing".
Is my surmise correct?