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One Sided Limits of Greatest Integer Function

  1. Sep 10, 2012 #1
    Can somebody tell me how to find one sided limits for greatest integer function, say Lim x->n-, [[x/2]]. that is limit x approaches n from left of [[x/2]] where [[]] represent greatest integer function and n is any integer.

    I know how to find one sided limits for simple [[x]].
  2. jcsd
  3. Sep 10, 2012 #2


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    If n is even, the limit is n/2. If n is odd, the limit is (n-1)/2.
  4. Sep 11, 2012 #3


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    The technical way is to use the epsilon-delta proof to show that you get all the properties for some delta and epsilon and so on.

    Since the function is continuous in-between the values of the integer points for these types of functions (floor, ceil, etc) then you can use math-man's answers provided above.
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