User:Cloudy176/Markov

Sample 1
e. Dimensional group - "lugion marks) - how up here, X^^X alone row, ex: {3,3,3 // 2 } - this to Array Notation.

Extending g-1 X-wing brackets around it, g is the airplane of all of the rules:

Dimensional spaces. These array of a's (3) b^3 array not represents a 3^^^3 array is {L,L,L,...X^(X^X+polynomial),...X^(polynomial),...L100,...L100,...etc. array, etc. array notations of legion space is shown by [ ] brackets)))))) - YIKES!!

Chris Bird has attempted to each other way beyond)

Currently I have been interested by a trimensional, heptational, explodotetration - last entry begins a row - (a,b (n)...(k) c #} = {# (n) a,b,c,...X^(polynomial),..... An} - here this is 1  - {a,b,c,...,k} = {a,b} = a^b was still use the initial rules for {L,X}b,p = {b,p / 2} = {a,a,a,...a{a,b-1 (n) ... (k)

Entry - a proof) this is a 3-D arrays can be concept of BEAFing up the pilot's it!! - much that is of highest entry in investigating n-D structure that I have developed a book, the {} and take on anythings there A is an X^X^X^X^X}} array remainder old very complicated to b = a power of entry - a strings are row of legions, Lagion space before the legion of arrays - or 2 entries - {a} = a multiplying, exponents an X^n structures, trime block of the BEAF, here the (n) ... (k) 1,1,..........b times (the airplane, previous array can use these kind that {A / 1} = A, so lets use the change into the new versions of a legions. They consist of entry - a pentonated to keep in mind the next levels which would has such as and appears to be {L,{L,2,2},1} = a, {a,b} = a, {a,b} = a+b Chris Bird's proof) that four imagine {L,n}b,p = {a,a,a,...a{a,b-1,c,d,...,k,1} = a, {a,b} = a power of itself 3^27 times - no pilot, all dimensional arrays (and possibly pentational to work it gets work with third smallest arrays, and the largest type that is of higher order - where the structure - these array notation, and solved as {b^4 array of a's (2) 5,4 (1)/ 2} = 3 to b = a{5}b (old version), from 1 "1" (3rd entry right before the 6th row of /'s it!! - much simpler way of 3's

{3,3 // 2} = {b&b&b&b&.....X^^^^````^^^X,...... Infinition - notice how the previous row of /'s is the 1's - the pilot. This will always include thing frontwards) third small, the prime entry (value of a's (2) b^2 arrays - and # for "lagiattic array, i.e. an X^X^X^X^X}^ arrays consists of planar, realmic, flunic, etc in the structures, the rules getting versional array is a tetrated to Conway's Chained A

Sample 2
,4, and 7. Boobolplex = {10,10,10,10,10,10,100,4}. Super dimension of dimensions. R^R^R = R tetrated to number. A boogol, sextoogol tens !!! - these numbers are definity like its go for this: starts to fill up the second row 1, and quintol.

Wompogulus. This is also be represented to itself" 98 times = 10^^^10 array where D is a 10 times" times" times" times. So a giggolduplex, and baggol, boogolplex = {10,100,n} where {3,3,3 (1) 2} and quadrol = {10,10,quadriggolplex is 10 tetrated to itself - 1 followed by "1 followed by 10 billion zeroes" zeroes" zeroes. - so the grand xappol Group - includes decated to comparison the size petossol = {10,10,10,2} = 3 10. This graphed like linear a gongulus = {10,goobolplex, missol, hexadecated to 3 = {10,10,10,beegol, quadrongulus, there Y is the big boowa - the grand Tridecalplex, googolduplex, xennossol, massol, treesol, gobbol, geebol, geetrol, quadroogolplex is 1 superdimensional arrays and gossolplex = {10,10,10,10,10,10,10 (1) 10,10,10 (gongulus, tridecalplex, terossol = {10,10,10,10 (1) 3}, and gongulusplex, and bagol. Below is a dimensional groups, (n,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 2} - where now at these numbers great big hoss //////.......go to {3,3,3 (1) 10,100} & 10 = ""10^100 array of tens that is a 10 = {10,10,10} = {10,10 (1) 10}. Diteralplex = {100,10 (1) 2} where n=2,3,4, and 5 respectively. Feel free to itself 10 times. Troogolplex = {10,10,hexadecalplex is 10^^100 = {10,truperdimensional array of dimensional arrays and a golapulus Group - includes dimendecal. We are n=2,3,4,5,6, and 9 dimension of dimensional array Notations meameamealokkapoowa and meamealokkapoowa and meameamealokkapoowa = {3,3 (1) 2}. Ultatri (pronounced DI ter al) = {10,10 (100) 2} where n=5,6, and boogolplex, Mega (Mega (Mega cal) is a sizes. Trimensional cube of tetrated to solve it's size. We can also coined on Rob's web page.

The Baggolplex = {10,10,10,10,10,10,100}, a golapulus = {10,10,10,100}. The grand will be reaches for gongulus) 2} - MUCH larger the 10 is bracketed a general = {10,10,10 (1) 4} and superpent, the much much small number, the corporal Group - includes the powerexploding a positive valued biggol, hexatri, quadroobol (1) 2} - includes triakulus, stage T2 - call this name came from the Corporal Group - includes the picture), continue this: start with big bootrol, quadraplex = {100,6}, goggol,6}, geegol, quadrunculus times, keep going out of tens in the defined by adding biggolplex = {10,100}10} - has 27

Sample 3
gh less trivial threw in the pilot (that's still on the definition of \omega^{\alpha \uparrow X!

The addition above!

Let's try k = \alpha_2} + \omega \uparrow X structure, which is merely \{a, b, 1, 1, e, f\}, b, \ldots\ \{\{a, b, 1, 1\} = \{a, b, b (1) c, d\}, d + 1\}, 1, d\} = b♦p / b♦p\} where the conception above nonnegative is per the prime. After the modern BEAF" by redefining what happens when v(A) = v(A').

Formally introduce a few. ◾ \alpha \uparrow a}_b. Here would be evaluated to l[n]. 2. Decrease than two legions is a break between zero and \beta + \omega^{\alpha + 1}) = \{0 \mapsto \omega^{\omega \uparrow\uparrow notational arrow notation. ◾ \{a, 1, c\} = a^b = \underbrace{n,n,n,\cdots, b, c, d\}, c\} for ordinary arrays.

Let's definition of A four-dimensional arrays if you are copilot and the numbers, so called a dimensional array are unchanged.

Another an entry of X^{m-2}, and in \{b, b, 1, 1, 1, d + 1\}[n] = \omega, \omega, so the prime block of define "order arrays

We have computer one of a legion space called X-structure them at that's still on the same, as in 3&3&3. This define A' as A, but it. Decreased by one. We'll cut to specify other number of definite array, but no base is the same plane. ◾ A(\sigma) := b forth. We'll take a moment some fundamental sequences to b. Here the same, and "array of operator notation space" using formalizing things like normal effect.) This natural for continue the passengers to ordinal, but it to a simple, 3\&4 has broken our previous structures, a, a\}_{\text{n n's}}\}.

Remember of b's), this is easy: ◾ \alpha \uparrow\uparrow\uparrow \omega) = \Pi(\pi) - 1},n - 1}, c + 1\}[n]

More rows

To continuing the fundamental sequences they work works up until we reach multiple plane.

This fundamental sequence \& with \zeta_0 = \omega^\omega2) = \underbrace{\{a, 1, c + 1\}\}\}\ a This step here is the unchange here, we used the seams. Equipped around 2002. The value of the expresses the primitive-recursive. \{b, p ///(1)/// 2\} or \{L, L / 2\} &=& \{3\}\ a\ \{a\}\}\ b = a \uparrow n} for limit of operators. This out as point is \omega, \{a, b - 1, c + 1} structure as one order intuitive concept of "structures.

Good the second p as {3, 3, 3}&3 (triakulus as (3&3)&3, and structure is stract terms. To keep this concise, we'll recursively, then v(A)[n]\} for d \in S. ◾\{a, b - 1, c, d\} = a^b and only for loops with b are not at X^{P + X^{n + 1}.