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Post by Admin on Jun 5, 2014 17:22:48 GMT
I created the psi function to simply the expression of the different dimensional separators (i.e. (1) ((3)) {3} {{{6}}} ) And I chose the greek letter Psi because I think it looks the coolest out of all of the Greek Letters
Ψ (a,b,c)The Psi function has 3 arguments, the first one "a" represents the order of the separator the second argument represents how many separators are nested in one another and finally, the third argument represents the number inside the separator if there are successive dimensional separators, (i.e. [a,b (1)(2)(3)(4) c,d] HC) the Psi function can be written as such Ψ (1,1,1)(1,1,2)(1,1,3)(1,1,4)ExampleΨ (3,2,1)=||1|| Ψ (2,4,8)={{{{8}}}}
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Post by Admin on Jun 5, 2014 18:01:39 GMT
I can now define the different properties of HC notation in a more simplified manner
[a,b Ψ(e,f,g) c,d]HC=[a,b Ψ(e,f,g-1) a,b Ψ(e,f,g-1)...Ψ(e,f,g-1) a,b Ψ(e,f,g-1)]HC
[a,b Ψ(e,f,1) c,d]HC=[a,b Ψ(e,f-1,[a,b Ψ(1,f-1,1) c,d]HC)(e,f-1,[a,b Ψ(1,f-1,1) c,d]HC-1)...(1,f-1,1) c,d]HC
[a,b Ψ(e,1,1) c,d]HC=[a,b Ψ(e-1,[c,d]HC,[a,b Ψ(e-1,[c,d]HC,1)) c,d]HC
There can be more entries in the Psi function
[a,b Ψ(e,1,1,1) c,d]HC=[a,b Ψ(e-1,[c,d]HC,[a,b Ψ(e-1,[c,d]HC,1)),1) c,d]HC
[a,b Ψ(e,1,1,1,1) c,d]HC=[a,b Ψ(e-1,[c,d]HC,[a,b Ψ(e-1,[c,d]HC,1)),1,1) c,d]HC
and so on and so forth...
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Post by Admin on Jun 7, 2014 0:03:17 GMT
The Psi function is given an order based on how many arguments there are in it Ψ (a,b,c) has 3 arguments and is a Psi Function of the 3 rd order Ψ (a,b,c,d)=4 th order Ψ (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p)=16 th order - The first argument is called the head argument
- The final is called the tail argument
- All arguments in between are called body arguments
- Body arguments are given numbers based on their position with respect to the head argument
- The first body argument is the argument closest to the head
- The second body argument is the argument to the right of that etc...
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