/sci/ - Science & Math

Okay let me explain this because I clearly didn't write enough for /mg/ to get it >>12270648

Suppose your method requires at most [math]n[/math] flips. You might use less than [math]n[/math] flips depending on earlier flips. Consider all allowed sequences of flips under your algorithm. What your algorithm is doing is assigning each allowed sequence to one of the three options. You might argue that you could ignore the order of flips (all or some of them), but then all that's happening is you're just assigning sequences which are permutations of each other to the same option.
Now suppose we modify the algorithm slightly. If there is a sequence of less than [math]n[/math] flips which we use to make a decision then modify the algorithm to keep flipping (until [math]n[/math] total flips) after the decision has been made but just ignore the later flips.
For example, maybe [math]n=3[/math] and your algorithm assigns HT to the first option. Then the modified algorithm assigns HTH and HTT to the first option. We note that the assignments from the modified algorithm have the same probabilities as the original one (this is the sum rule of probability).
The modified algorithm is an assignment of each element of [math]\{0,1\}^n[/math] to one of the three options. Since each element of [math]\{0,1\}^n[/math] has equal probability ([math]2^{-n}[/math] the algorithm must partition [math]\{0,1\}^n[/math] into three equal sets if we want there to be an equal probability. This is impossible as 3 does not divide [math]|\{0,1\}^n|=2^n[/math].

Please /mg/, this is not a difficult proof to understand. I'm happy to answer any questions you have about it. If I see one more fucking person claiming it is actually possible...

>>12224141
This was the top result I found googling "mathematician big five personality":
>https://www.sciencedirect.com/science/article/abs/pii/S0191886913006132
>Among Big Five factors, Openess was the best predictors of test performance
There's a bunch of papers that I can link you after you debunk this ones methodology. I would love you to post some of your own evidence though!

>>12213912
A bloo bloo bloo