Ndryshimi mes inspektimeve të "Përdoruesi:Armend/nënfaqe"

(M\{\}\,)
Denote by <math>N=\{0,1,2,...\}\,</math> the set of natural numbers and by <math>I_m=\{0,1,...,m-1\}\,</math> the set of natural numbers lesser than given natural number m. Lets <math>c=(c_0,c_1,...,c_{m-1})\,</math> a m-sequence of natural numbers and <math>p=max\{c_0,c_1,...,c_{m-1}\}\,</math> the greatest term of sequence c then the sequence
 
:<math>t(c)=(t_0,t_1,...,t_p)\,</math>
 
where <math>t_j,j\in I_{p+1}\,</math> denote number of terms of sequence c thats are equal at j, is called trace of c. Is clear that terms of trace fulfills the conditions
 
where denote number of terms of sequence c thats are equal at j, is called trace of c. Is clear that terms of trace fulfills the conditions
 
:<math>t_0+t_1+...+t_p=m\,</math>
:<math>t_1+2t_2+...+pt_p=c_0+c_1+...+c_{m-1}\,</math>
 
Denote by
 
:<math>t^{0}(c)=c\,</math>
:<math>t^{n}(c)=t(t^{n-1}(c))\,</math>
 
1. The set of sequences is called bracelet of sequences and for each sequence c from B holds
 
:<math>B=\{(1,0,0,1),(2,2),(0,0,2),(2,0,1),(1,1,1),(0,3)\}\,</math>
Because
 
2. Thethat setis ofcycle sequencesof length 6 is called ring'''bracelet of sequences''' andbecause for each sequence c from RB holds
2. The set of sequences is called ring of sequences and for each sequence c from R holds
 
:<math>t^6 (c)=c\,</math>
Because
 
 
2.The set of sequences
The set is called black hole because for each finite sequence a of natural numbers exists natural number n such that in other words each sequence converges to H.
 
Sequence a is of type B if its converge to H from B for example sequence (2,3) is of type B because
:<math>R=\{(0,1,1),(1,2)\}\,</math>
 
that is cycle of length 2 is called '''ring of sequences''' because for each sequence c from R holds
 
:<math>t^2 (c)=c\,</math>
 
 
The set
 
<math>H=B\ cup R\,</math> is called ''' black hole of sequences'''
 
Reasons for that name are because I suppose that:
 
The set is called black hole because forClaim:For each finite sequence <math>a\,</math> of natural numbers exists natural number n such that <math>t^n(a)\in H\,</math> in other words each sequence converges to H.
 
Sequence <math>a\,</math> is of type <math>B\,</math> if its converge to H from B for example sequence (2,3) is of type B because
 
: <math>t^3((2,3))=(0,0,2)\in B\,</math>
 
And sequences that converges to H from R are of type R for example the sequence (0) is of type R because
 
:<math>t^6((0))=(1,2)\in R\,</math>
And sequences that converges to H from R are of type R for example the sequence (0) is of type R because
 
 
WeMy canquestion seeis.Is thatmy allassumption sequencestrue thatsand followif (0)it areis of type R. My question istrue how to decide of which type is any given finite sequence of natural numbers, can be done any programme or algorithme. Thanks