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Thread: partition line

  1. #1 partition line 
    Forum Sophomore
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    if aline is partitioned into infinite parts.can you measure length of each part?


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Depends on how you partition it.


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  4. #3 Re: partition line 
    . DrRocket's Avatar
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    Quote Originally Posted by parag1973
    if aline is partitioned into infinite parts.can you measure length of each part?
    MagiMaster's answer is precisely correct. It is possible to partition the line into distinct sets, called non-measurable sets, for which the notion of length (size) makes no sense. But most partitions of the line that one sees in practice involve only measurable sets, and one can define a notion of size for those sets that coincides with your intuitive notion of length. It actually takes some work (and the axiom of choice) to demonstrate the existence of non-measurable sets.

    Depending on the particular partition into measurable sets, some of the sets may be of infinite length. In fact all of them may be of infinite length.
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