idk

[haughty iris]

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[crisp berry]

i don’t suppose you’ve heard of rearrangement inequality?

[woeful river]

could you enlarge the picture a bit

[crisp berry]

the denominators are x2, x3, …, x1

[spiral vector]

i havent

[crisp berry]

ok

cauchy?

[woeful river]

oh makes more sense now

[spiral vector]

I forgot about it

[crisp berry]

ok

rearrangment inequality basically states that if you have two sequences, and you pair terms from them, multiply, and then add the results, the largest value comes when the largest terms are paired together

if you like, i could give an example?

[spiral vector]

sure

[crisp berry]

before you are three piles of money: one pile of &5, one pile of $10, one pile of $20
i tell you to choose 3 notes from one pile, 2 from another, and 1 from the third
how do you maximize your money?

[spiral vector]

3 from $20, 2 from $10, 1 from $5?

[crisp berry]

perhaps, obviously, you will choose 3 of the $20 note, two of the $10, and three $5s

yes

how would you minimize it?

[spiral vector]

3 from $5, 2 from $10, 1 from $20

[crisp berry]

yep

so if you have, for example, two sequences:
a1, a2, …, an
b1, b2, …, bn
then a1b1 + a2b2 +… will be maximized if the largest a is paired with the largest b, the second largest with the second largest, etc.

and the opposite for when it is minimized

[spiral vector]

yes

wait a minute

i might've got it

Oh i got it

ty

+close