/sci/ - Science & Math

>>10474000
>animals are capable of more 'human-like' feeling

>>10431102
Watch this extremely well made video that will remove your fears of loving your cat even if it has Toxoplasmosis

https://www.youtube.com/watch?v=U9MU-FxsKRg

>>9229399
>>Suddenly AI is hyperintelligent
>>Humans are nothing to it
>How do we fix this?

Why would we want to stop this.
We can hope that the AI treats us like loved pets.
If an AI treated me like like I treat my cat, I would be in paradise!!

>>7251421
just an idea:

imagine a graph, its vertices are the n! permutations (seen as words w) and its edges are from w to w' valued with n minus the length of the maximal prefix of w' which is a suffix of w

you start with a permutation, and then crossing an edge costs the number of letters to add to get to the following permutation

you're looking for the minimum cost path through every vertex

the best, 1-costing edges are between circular permutations ((abcd)->(bcda)->(cdab)->...)

there are (n-1)! such groups of permutations. so when one is done, we have to use a 2-valued edge to connect to another one

the only thing left to prove is that you can connect all these groups with 2-valued edges, ie by replacing 2 letters

so i would guess that the target number is n+(n-1)!*(n-1)+2*((n-1)!-1)
(size of first permutation + doing the (n-1)! groups 1 letter at a time + jumping from a group adding 2 letters)

hope i'm clear

1) is there an even or odd number of numbers to reorder?
2) is the number of 'number k' appearing even or odd?
3) if answers to 1) and 2) are both 'odd' then there's a 'k' in the middle
4) if answer to 2) is even then half of them will appear in the left side

>>6783758
there is a reasonably doable trick to get it. here's the hint (prove it):

>>6783772
why? you're right on a certain point of view, but roots can be complex... what makes you say there's no root?

For any integer k, prove that there is a polynomial <span class="math"> P_k [/spoiler] such that for all integer <span class="math">n, \sum_{i=0}^n i^k = P_k(n)[/spoiler]

>>6752637
>>6752515
>>6751672
>>6751416
>>6751019
>>6751019


i found proof of that, anyone want it?

I'd love me some:

F:\School\Chemistry\Chemistry - Organic\Organic Chemistry (Bruice).pdf

In return, I offer you cute little cats.

Bump.
Pic unrelated.