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Thread: What's the point of subscripts used in Computer Science?

  1. #1 What's the point of subscripts used in Computer Science? 
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    What do subscripts mean in Computer Science? I am studying the Design and Analysis of Algorithms (I am starting the course) and I don't know what the following means:

    Big O-notation: f(n) = O(g(n))
    if there exists positive constants c, n0 such that
    f(n) <= cg(n) for all n >= n0.

    For n0 the 0 is in subscript.

    What does the n0 mean? We know that n is a variable, so why so we have to define that it is less than another variable? And why is it called n0? Why not call it something else? Doest n0 simply mean the first and minimum value of a possible value range or list?

    Appreciate if anybody can help me out with this, that has studied and Algoirthms Course a bit or knows this.


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  3. #2 Re: What's the point of subscripts used in Computer Science? 
    Forum Ph.D. Leszek Luchowski's Avatar
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    Quote Originally Posted by fwonger
    Doest n0 simply mean the first and minimum value of a possible value range or list?
    I don't know why you said "possible", but except for this word, the answer is yes. This n0 is the first and minimum value of a range of natural numbers, starting at n0 and never ending.

    So your definition says that such and such conditions must be met for all natural values of n starting from somewhere.

    The condition might, for example, not be met for n=1, 3, 28, 43, 85 and 113 (I am taking these values from the back of my head), but there is a number, say 121, such that for this number and for all natural numbers after it the condition is met - then your definition applies.

    Why they chose to call it n0? Why not? It might seem more obvious to call it n1, as it is the first of the range, but computer folks often number things starting from zero rather than one.

    Hope this helps,
    Leszek.


    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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  4. #3 Re: What's the point of subscripts used in Computer Science? 
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    Quote Originally Posted by Leszek Luchowski
    Quote Originally Posted by fwonger
    Doest n0 simply mean the first and minimum value of a possible value range or list?
    I don't know why you said "possible", but except for this word, the answer is yes. This n0 is the first and minimum value of a range of natural numbers, starting at n0 and never ending.

    So your definition says that such and such conditions must be met for all natural values of n starting from somewhere.

    The condition might, for example, not be met for n=1, 3, 28, 43, 85 and 113 (I am taking these values from the back of my head), but there is a number, say 121, such that for this number and for all natural numbers after it the condition is met - then your definition applies.

    Why they chose to call it n0? Why not? It might seem more obvious to call it n1, as it is the first of the range, but computer folks often number things starting from zero rather than one.

    Hope this helps,
    Leszek.
    Thanks.

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  5. #4 Re: What's the point of subscripts used in Computer Science? 
    Forum Ph.D. Leszek Luchowski's Avatar
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    You are very welcome.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
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