aka Super God Genus borakan Psi the 5th.

  • I live in Everywhere and Knowhere.
  • My occupation is My occupation is king of the Omniverse
  • Primussupremus

    Last time I talked briefly about the fact that symbols produced from each subsequent vocabulary of symbols is 1 less the letter value than the letter preceding it. Now I'm going to describe a generalization of this vocabulary rule.

    For any set of length x>=3 and of the form (x,y,z,w,v,u...) , there exists a unique division of the set into the form.

    {a,(x,y,z,w,v,u...)b}R{a,(x,y,z,w,v,u...)b} such that everything in the ()'s has 1 less symbol than the combined set.

    For example: {2,(4,4,4),8} = {2,(4,4),8}R{2,(4,4)8}.

    But suppose that we want to extend beyond simple linear expressions?

    We need to define a new symbol and rule. [] [{a,(x,y,z,w,v,u...)b}] = {a,(x,y,z,w,v,u...)b} recursed into () {a,(x,y,z,w,v,u...)b} number of times.

    To give an examp…

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  • Primussupremus

    Since I have been away from this wiki for what seems like years and forgotten almost completely about my old notation I decided to start anew with a brand new notation which I call alpha array notation.

    Since I've "literally" just thought about this notation a few minutes before writing these words I won't develop a rule set until later on since I don't want to rush into things.

    First of all we need to start at the bottom and work up.

    I have decided to call this regiment the unary regiment and with it comes the unary vocabulary.

    The unary vocabulary is listed as so:

    • { } are used to hold the array in place.
    • Variables {a,b,c...z ,a,c,b,....z , b,a,c,....z, b,c,a,....z and so on) are used to represent values in which to input into the array.
    • numbers…
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  • Primussupremus

    Can someone explain explain to me how the SKI combinator calculus works because when I try to understand it is goes over my head ,I would also like to know how it can lead to functions such as Ξ function which grow uncomputably fast?

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  • Primussupremus

    The name of this number is Sindadrin-x. Its value in my notation is {10:↑((ω^(ω^2))(10)}.

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  • Primussupremus

    This is part 2: I will be starting at {K:↑(ω+1)(X)} then moving on from there.

    {K:↑(ω+1)(X)} = {K:↑(ω)(X)} recursed ({K:↑(ω)(X)}-1) times.

    {K:↑(ω2)(X)} = {K:↑(ω+ω)(X)}= {K:↑(ω+X)(X)} = {K:↑(ω+X-1)(X)} recursed ({K:↑(ω+X)(X)}-1) times.

    {K:↑(ω3)(X)}= {K:↑(ω2+x)(X)} = {K:↑(ω2+X-1)(X)} recursed ({K:↑(ω2+X-1)(X)}-1)times.

    {K:↑(ω^2)(X)}= {K:↑(ω*ω)(X)}= {K:↑(ω*X)(X)} = {K:↑(ω*X-1)(X)} recursed ({K:↑(ω*X-1)(X)}-1) times.

    {K:↑(ω^ω)(X)} = {K:↑(ω^X)(X)}= {K:↑(ω^X-1)(X)} recursed ({K:↑(ω^X-1)(X)}-1)times.

    {K:↑(ω^ω+(1))(X)} = {K:↑(ω^ω)(X)} recursed ({K:↑(ω^ω)(X)}-1) times.

    {K:↑(ω^ω+(ω))(X)} = {K:↑(ω^ω+(X))(X)} = {K:↑(ω^ω+(X-1))(X)} recursed ({K:↑(ω^ω+(ω))(X-1)}-1) times.

    {K:↑(ω^ω+(ω+1))(X)} = {K:↑(ω^ω+(ω))(X)} recursed ({K:↑(ω^ω+(ω))(X)}-1)times.


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