[Arcaea] Hardest Free Song - Aleph-0 Pure Memory [Future 10] 

FIRE IN THE HOLE🔥🕳️🕳️🔥 FIRE IN THE HOLE🔥🕳️🕳️🔥

@@MRGPL.HikariFIRING IN HOLES 🔥🔥🔥🕳🕳🕳🗣🗣🗣

Ur good at math right?

@@YUO77999 It's not like that, I saw it in a book

0:29 여기서 나온 것은 가산집합입니다.

@@noname-js5uj 피드백 감사합니다

@@Rainz4_3oX Make an run for it… *DEADDEADDEADDEAD* Never turn back… *DEADDEADDEADDEAD*

do u know y the original wasn't used?

@@iamghostorami I'm really curious why tbh, because I also don't like their version

What about chronicle? I find that 10 a lot harder than aleph 0.

mathmo in training here (first year uni maths is killing me) If a set is countable, you can map each object in a set to a natural number. (this is called an injection) An example would (quite unintuitively so) be the rationals. We can first simplify all the fractions, then map it using a function such as f(x) = 2^(numerator)*3^(denominator), that way every fraction is mapped onto an integer and is thus countable. (there’s a further mapping to be done from integers to naturals but i cba) If a set is uncountable, then this “injection” does not exist. An example of this would be the real numbers (see cantor’s diagonal argument) EDIT: changed some “bijection” to “injection” god i have so much revision to do

​@@ρωρ Actually rationals and naturals are of same size (countable) since you can construct a well-defined bijection between them, this works for both even numbers and odd numbers too. However irrationals and real numbers are not of same size to naturals.

같은 노란색이길래 넣어봤어요 ㅎㅎ

i lost it at that part lol

I would upload a play video some day. Already unlocked it

5

It’s not free

​@@SpeedyStyleWell it was free tho, it's a World Extend song just like this one. The BYD also doesn't require paid songs so in a way it's free. Plus, Aleph-0 is no longer free now so it's in the same situation as Purple Verse

It’s free if you unlock it in world mode during an event

지금은 무료 이벤트 기간 끝났어요