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Consider a computer system that has $m$ number of objects in its memory. Job of the system is to search the specific object. We describe all searchable objects in the memory as a set $\mathscr{A} = \{1,2,3,.....m\}$.

So if in first cycle system does not locate the object, It will traverse the $\mathscr{A}$ again. In second cycle we suppose system again failed to find the object in the set then system traverse $\mathscr{A}$ again. System will keep traversing that set for $n$ number of cycles until it finds the specific object.

If we describe set as $\mathscr{A_i} = \{1,2,3,.....n_i\}$, Then reputation behavior can be described theoretically as

$\mathscr{A_1} = \{1,2,3,.....m_1\}$

$\mathscr{A_2} = \{1,2,3,.....m_2\}$

$\mathscr{A_3} = \{1,2,3,.....m_3\}$

$. . . . . . . .$

$. . . . . . . .$

$\mathscr{A_n} = \{1,2,3,.....m_n\}$

If set of elements in form of variables for example $\mathscr{A} = \{a_{11}, a_{12}, a_{13}\, . . . ., a_{1m}\}$ , Then how can we describe the repetition behavior of the set theoretically?

William Elliot
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Bilal Mirza
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    Objects in memory are better represented as sequences or lists, not as sets. – lhf Sep 29 '18 at 17:29
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    I am making analytical model for system behavior, I have a data set that gets traverse in a linear order. I have to provide time complexities of each case. I am asking about theoretical description. – Bilal Mirza Sep 29 '18 at 17:32
  • This is not off-topic. Just slightly confusing. Leaving open. @AhmadBilal Could you make clearer what you mean by the repition of set elements – Nick Sep 30 '18 at 01:26
  • I am working n research paper, in which system reduces the set size after each traverse cycle. In next cycle set is the same but its elements get updated and get reduced as compare to previous cycle. Now I have to provide analytical model for Best, Average and Worst cases for each cycle. For example 1st, 2nd .... and nth cycle of traversing on same set. – Bilal Mirza Sep 30 '18 at 06:53
  • May be I have confused the community by disusing the problem with computer memory reference, It is pure math problem. – Bilal Mirza Sep 30 '18 at 07:01

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