[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math


View post   

File: 23 KB, 647x644, jykurih1gjc11.jpg [View same] [iqdb] [saucenao] [google]
11113193 No.11113193 [Reply] [Original]

Proof that [math]g(TREE(64))<TREE(g(64))[/math]

Let the function [math]g(n)[/math] be defined recursively such that
[math]
g(n) =
\begin{cases}
g(1)= 3 \uparrow\uparrow\uparrow\uparrow 3 & n = 1 \\
g(n)= 3 \uparrow^{g(n-1)}3 & n> 1
\end{cases}
[/math]

Where [math]g(64)[/math] is Graham's Number. By the Brady's Power Juice™ function [math]J(n)[/math] ,we can observe by sheer mathematical intuition, that [math]g(TREE(64))[/math] has less juice that [math]TREE(g(64))[/math]

[math]
J(g(TREE(64))) < J(TREE(g(64)))
[/math]

Then, by the Juice theorem, which states
that, for any two integers [math]m,n[/math]

[math]
J(n)>J(m)\Rightarrow n>m
[/math]

We follow that

[math]
g(TREE(64))<TREE(g(64))
[/math]

Q.E.D

>> No.11113194
File: 112 KB, 640x730, 1834682878272.jpg [View same] [iqdb] [saucenao] [google]
11113194

>>11113193
>OMG!! BIG NUMBERS DUDE!!11!!!

>> No.11113197

>>11113193
I hate to admit it but you've got 50% of being right

>> No.11113202
File: 164 KB, 498x497, bad[1].png [View same] [iqdb] [saucenao] [google]
11113202

>>11113194
where n is the largest number used on any numberphile video, let anon's number [eqn]A=n+1[/eqn]

>> No.11113203

Im obsessed with proving that bill nye the science guy is illegitimate due to my high iq

>> No.11113206

>>11113194
>has all the ingredients to make a sandwich but can't make a sandwich
>has also mastered faster than light travel
>k

>> No.11113213
File: 37 KB, 325x481, B1634718-9EDC-45B1-BA19-050B69CE9DBD.jpg [View same] [iqdb] [saucenao] [google]
11113213

“Not a scientist”

>> No.11113230

>>11113194
Is droning on about BIG NUMBERS the most midwit and I FUCKING LOVE SCIENCE tell ever?

>> No.11113943

>>11113230
Perhaps, but the recent video about the growth rates of these functions like [math]g[/math] and [math]\mathrm{TREE}[/math] was actually quite interesting. From what I understand, you have to develop a whole new hierarchy of ordinals in order to meaningfully classify these objects.