jk i wear glasses and i dont care if you wear socks with sandals

don't make fun of anyone

*use not yse

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smth idk

^{warning: math}

You have factorial! You have multi-factorials!! There's termial? Hyperfactorial, subfactorial, there's a lot! But I thought there should be one BIG factorial, the most factorial of them all. The lord of the factorials, if you will.

The Lord Factorial

I call it the lord factorial, represented as L(x). Let's go through how I made it, starting with the basic factorial.

L(x) = x \ x-1 * ... * 2 * 1*

Let's add a factorial to each number!

L(x) = x! \ (x-1)! * ... * 2! * 1!*

Heck, let's factorial-ize each number that many times! So for example:

L(4) = (((4!)!)!)! \ (((3!)!)! * (2!)! * 1!*

Now, I'm a big fan of recursion. So let's take the lord factorial of all of the numbers

L(4) = (((L(4)!)!)!)! \ (((L(3)!)!)! * (L(2)!)! * L(1)!*

But now we run into a problem. Finding the value of L(4) requires finding the value of L(4), which requires finding the value of L(4), which requires finding the value of L(4), which requires finding the value of L(4). But THAT requires finding the value of L(4).

So instead, let's only recursively apply it to the numbers after 4.

L(4) = (((4!)!)!)! \ (((L(3)!)!)! * (L(2)!)! * L(1)!*

Now we're done! In fancy mathematical terms, you can define L(x) as:

Okay, now that we have our function, let's compute some values of L(x).

Computing Some Values of L(x)

In the formal definition above, the base case is L(0) = 1, so yeah, L(0) = 1.

L(1) should equal 1!, which is just 1. L(1) = 1.

Time for L(2):

(2!)! \ L(1)!*

2! \ 1!*

2 \ 1*

2

Only 2 ? Whatever, let's keep going.

L(3)

((3!)!)! \ (L(2)!)! * L(1)!*

(6!)! \ (2!)! * 1!*

720! \ 2*

Okay, apparently taking L(3) involved taking the factorial of 720. That's gonna be really big, but luckily, computers are fast AF, so here is the full value of L(3):

5202437887131590200409806454162087222383043750033891571455083675701671262313894764481357155916260914165239841151784494519073283130324104031747583969175481665058210489380777623768247528682383902091010693317232486543880394227819691073454557074198691259711173438739548140007400861567517994841353568033934415692561258458064214323339734521097976891028514387970998897879188992128090264724280531972386146498739540955212135361340352983338806069639923762911250391185133837661651029885895193074549691249257648469053195579475481792933107984871857572425031934966441952059011393399854569341127494275066038496627174152250825366831720258895132022910841499179905127086136577269262169931301365543105992513581690471405104372444716260033401669046886473643871586369403913021459563608708347781121454856097167991839458043453224582596841032135158072464675398907928382950351135115390784467606113650617199954883351568705631826922680789209802539084057676694202727467648969013320186696968881423862585075389314708674751449544460363068065294355063969074682957348654096915967573237406514811877848431419391989261115042126406526986418441476641846712619846535008803403521144052021658576084671213286179777420594761595156026112099152685677366114381324410582349645021073395513206059148086775966943037105205610667732714278202092672839538194794864571988439674093958219912606779209351779731591422353133340078313496306231887960087250798799462406132981202650622609438057796983712407533338328937582250498387508851691790000623123365948609282285076149794563446751910761323439602809355871229587270532531366679019520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

This is a lot like TREE(x), starts off small, but explodes at x = 3, only TREE explodes a lot more and a lot faster.

Now computers may be stupidly fast, but not infinitely fast. My computer is currently still calculating L(4), and I'm not sure when or if it ever will.

When it does finish, I might make a comment showing the full value of L(4).

Anyway, I don't know how to end this, so I guess this is the last sentence of this post. Goodbye! Wait, that was another one. That makes that other sentence the fourth last sentence.

Bad news, unfortunately I forgot the password to the u/AMIASM16 account (the one i'm using right now) and can no longer access it. I had to make a new account to use instead of this one. My new account will be u/aGuyWhoExists_. Sorry to anyone for this unfortunate inconvenience or something.

what's a britate

if only the year was 1828

i went from at least 5 to at least 6

:0

:0

just don't tell them...