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That's the absence of proof. It's a bit different from the proof of a negative. Don't worry you're not the first one mentioning it so that's something that mus
by aatd86 3y ago
That's the absence of proof.
It's a bit different from the proof of a negative.
Don't worry you're not the first one mentioning it so that's something that must be some kind of colloquialism somewhere but I was asking to understand what people may have meant.
To top it all, you proved a negative (by providing a counterexample) :o)
- mort96 3y agoNo, it's absolutely a proof. Claim: There is no odd number in {2, 4, 6}. Proof: 2 is not an odd number, 4 is not an odd number, 6 is not an odd number, there are no other elements in {2, 4, 6}. Therefore, there is no odd number in {2, 4, 6}. If there was simply an absence of proof, we would be forced to conclude that we don't know whether there's an odd number in {2, 4, 6}. That's clearly not the case. The claim "S is a set with no odd number" is equivalent to the claim "S is a set where all numbers are even", which is something I assume you agree that we can prove.
- aatd86 3y agoI'm not talking about the first part of the comment but the latter parts regarding the general case. (I even wrote that he proved it himself at the end)