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what would be the function of the graph with contains all the intregral values of the universe.????

what would be the function of the graph with contains all the intregral values of the universe.????

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1 Answers

AKASH GOYAL AskiitiansExpert-IITD
420 Points
13 years ago

 

 

Dear Indrajit

greatest integer function

  • The greatest integer function of a real number x is represented by [x] or |_x_|.

     

  • For all real numbers x, the greatest integer function returns the largest integer less than or equal to x.

    In other words, the greatest integer function rounds down a real number to the nearest integer.
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More about Greatest Integer Function

  • Greatest integer functions are piece-wise defined.

  • The domain of the greatest integer function is the set of real numbers which is divided into a number of intervals like [-4, 3), [-3, 2), [-2, 1), [-1, 0), [0, 1), [1, 2) , [2, 3), [3, 4) and so on.

     Hint: [a, b) is just an interval notation which means a ≤ x < b, where x is a real number in the interval
             [a, b).
     
    When the interval is of the form [n, n + 1), where n is an integer, the value of the greatest integer function is n. For example, the value of the greatest integer function is 4 in the interval [4, 3).

    •
  • The graph of a greatest integer function is not continuous. For example, the following is the graph of the greatest integer function f (x) = |_x_|.

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    All the best.

    AKASH GOYAL

    AskiitiansExpert-IITD

     

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