4 ms·
While I agree with you, in the context of a "hand wavey" explanation, "more" is not rigorously defined and so saying "plain wrong" is silly. A strict subset rel
by j2kun 8y ago
While I agree with you, in the context of a "hand wavey" explanation, "more" is not rigorously defined and so saying "plain wrong" is silly. A strict subset relationship is a reasonable interpretation of "more" in the context of an informal discussion.
- Grue3 8y agoLeaving aside the fact that talking "informally" about infinities easily leads to wrong conclusions, the OP wasn't even talking about a strict subset relationship. The comparison was between a set of proofs and a set of facts, which are sets of different mathematical objects. So at best you can say that each proof proves a fact (a fact can have several proofs) and the set of facts that have a proof is a strict subset of all facts. Or, informally, there are more facts than facts which can be proved. Oh, wait, this just restates the theorem we're trying to prove in the first place and doesn't give any insight into why it's correct.
- Sniffnoy 8y agoYes, but the use of "which in turn" suggests that was not meant; it suggests that what follows is a real deduction and not a mere rephrasing.