> If all groups of k people had the same age, then everyone in G except P would have had the same age. That is a true proposition ('false => true' is true)
The logical formula is right but the premise is wrong. But 7 is considering both.
It's like saying "Person P had 1Mi dollars and got 10% interest last year then now Person P has 1100k dollars". But Person P didn't. The interest calculation is correct, but the premise is wrong.
> The greater point of the excersise is to show a failure mode of an inductive proof.
I see that, but the fact that the other steps are not contributing to the solution makes it harder to argue that the mistake is there. Because that statement needs a qualifier, but it is "not wrong" per se (it's not even affirming anything, it's just saying "pick the person you haven't picked (from a group that might not have anyone else to pick, fair enough)
But everything derived from a false premise can be false. That's how we get the proofs by contradiction, right? We keep going down the wrong path until it obviously blows up
Or we could just prove this whole problem false with a set of two people in Canada with different ages (counterexample to Step 5). Case closed.
> It's like saying "Person P had 1Mi dollars and got 10% interest last year then now Person P has 1100k dollars". But Person P didn't. The interest calculation is correct, but the premise is wrong.
No it is not like that. It is like saying "IF person P had 1Mi dollars and got 10% interest last year THEN now Person P would have 1100k dollars". This statement is true regardless of how much money person P has today. That is how steps 5-8 work: they are true regardless of the truth of the antecedent ('in every group of k people, everyone has the same age'). Finding 2 people in Canada of the same age would NOT prove step 5 wrong (though it would show it to be pointless, of course).
Probably a much more interesting problem would have found a less obviously wrong premise to demonstrate this with. I'd love to find a way to build a similar argument for Fermat's last theorem or some other non-trivial observation.
The logical formula is right but the premise is wrong. But 7 is considering both.
It's like saying "Person P had 1Mi dollars and got 10% interest last year then now Person P has 1100k dollars". But Person P didn't. The interest calculation is correct, but the premise is wrong.
> The greater point of the excersise is to show a failure mode of an inductive proof.
I see that, but the fact that the other steps are not contributing to the solution makes it harder to argue that the mistake is there. Because that statement needs a qualifier, but it is "not wrong" per se (it's not even affirming anything, it's just saying "pick the person you haven't picked (from a group that might not have anyone else to pick, fair enough)
But everything derived from a false premise can be false. That's how we get the proofs by contradiction, right? We keep going down the wrong path until it obviously blows up
Or we could just prove this whole problem false with a set of two people in Canada with different ages (counterexample to Step 5). Case closed.