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Finity and Beyond
 1. IntroductionBig number that are so huge and complex, I can't defined it properly (and I can't understand it properly). I don't even know that such number exist or provable. And of course, the number here is salad-y number (using existing number to define new number, an heresy act for Googologist). However, though experiment is fun. So, ikuzooo! 2. Unproved Function2.1. Extension of Graham-Ramsey NumberThe infamous Graham number arise from the upper-bound on the answer of a problem in the mathematical field of Ramsey theory. Connect each pair of geometric vertices of an n-dimensional hypercube to obtain a complete graph on 2n vertices. Colour each of the edges of this graph either red or blue. What is the smallest value of n for which every such colouring contains at least one single-coloured complete subgraph on four coplanar vertices? However, the original problem only have two distinct color, red and blue. Let m represent the number of color in those spesific problem. Thus, the upper-bound answer of Ramsey problem is called "Extension of Graham-Ramsey Number". We will call it "The E number". E stands for "Extension". This new problem is called modified Ramsey problem. Connect each pair of geometric vertices of an n-dimensional hypercube to obtain a complete graph on 2n vertices. Colour each of the edges of this graph with m different colour. What is the smallest value of n for which every such colouring contains at least one single-coloured complete subgraph on four coplanar vertices? Thus, E(m) defined as the upper-bound on the answer of a modified Ramsey problem with m different colour. We can, hereby, define a larger function:
E2(m)=E(E(m))
En(m)=E(E(E … E(m)) …)⏠⏣⏣⏣⏣⏣⏡⏣⏣⏣⏣⏣⏢n
E0(m)=E(m)
E1(m)=En(m)
E2(m)=Enn(m)
Ea(m)=Enn⋰n⏠⏣⏣⏡⏣⏣⏢a(m)
 2.2. Extension of Kruskal's Tree TheoremWhat if we have k-dimensional Kruskal's Tree Theorem, since TREE(n) function we know are on 2D plane? I can't even think of… 3. Uncomputable Function3.1. Extension of FOST(x)The infamous Rayo's number defined as following The smallest number bigger than any number that can be named by an expression in the language of first-order set-theory with less than a googol (10100) symbols. There are two areas we can improve. First one is clear: the number of symbols. Second one is the language that define Rayo's number itself, first-order set-theory. What if, we have second, third, fourth, nth, and even Rayo's number-order set-theory? Absolute humongous! Usually, Rayo's number defined as Rayo(10100) or FOST(10100), where FOST stands for first-order set-theory. We will define any arbritarily large order of set theory to surpass Rayo's number. However, these definition is very ill-defined ... no, it's worse than that! Dead Defined! Since I know nothing about the order of set theory and its relaltion with how big the number that are produced. Anyway,
s1(n)=FOST(n)=Rayo(n)
s2(n)=second-order set-theory(n)
s3(n)=third-order set-theory(n)
sm(n)=mth-order set-theory(n)
s(n) stands for "set", it measure the number defined by Agustin Rayo in certain language of set-theory. m in sm(n) indicates the number of order in certain language of set-theory.