3 ms·
Looks to me like there are errors in the transformation. The sum term corresponding to the resulting equation of the proof has a wrong sign in the second summan
by nuclx 10y ago
Looks to me like there are errors in the transformation. The sum term corresponding to the resulting equation of the proof has a wrong sign in the second summand of the left term (+ instead of -). Also in the original manuscript the right side always starts with a positive alternating series term, which is correct. In the version on the margin the sign of the first term of the right side depends on the evenness of a.
- airesQ 10y agoI see your point. There are indeed a couple of errors in there. But the point still holds. The sign is wrong on the sum of the left hand side. And a (-1)^(a+1) is missing on the RHS. But these do not change the "this is an integer" claim. Further down, it does assume that 'a' is even, without saying so . But if 'a' was odd, things would still be the same but we would have a ]-1,0[ interval. Anyway, I'm not a mathematician so I'm probably missing stuff.
- mvf0 10y agoThank you for confirming this. These kind of errors drive me crazy when I try to work through proofs on my own.