Përdoruesi:Armend/nënfaqe: Dallime mes rishikimesh
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Rreshti 95:
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.
:<math>B=\{(1,0,0,1),(2,2),(0,0,2),(2,0,1),(1,1,1),(0,3)\}\,</math>
▲2. The set of sequences is called ring of sequences and for each sequence c from R holds
:<math>t^6 (c)=c\,</math>
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:
▲
▲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
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