Great video ! I think you got a bit confused in the end, as i feel like the inequality should be the other way around. Let c verify the equation, then from what you have proven, Sum^2 >= c sum^3 (You wrote the reversed inequality) . so c
i think the proof from this stems from the proposition about the fact that there are only n-1 pairs which create a sum of n, so the pairs which i created exhaust those minimal cases
I'm sorry to burst your bubble mate but the hard part is proving the minimal construction, evaluating that construction is not that hard since it is just a rational function that monotonically decreases.
Great video ! I think you got a bit confused in the end, as i feel like the inequality should be the other way around. Let c verify the equation, then from what you have proven, Sum^2 >= c sum^3 (You wrote the reversed inequality) . so c
then to prove that c is exactly 2/9, it shouldn't be so hard
oh yep! i donht know how i didnt catch that thanks
How did you prove that such a construction achieves minimality?
i think the proof from this stems from the proposition about the fact that there are only n-1 pairs which create a sum of n, so the pairs which i created exhaust those minimal cases
past the 2nd proposition it was mostly just pray and hope what i said was true
epic cool and based :D
Sigma
I'm sorry to burst your bubble mate but the hard part is proving the minimal construction, evaluating that construction is not that hard since it is just a rational function that monotonically decreases.
thats true i guess, although harder questions are definitely a new area for me so ill get there eventually