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Thread: Greatest Integer in Set Type

  1. #1
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    Greatest Integer in Set Type

    Greatest Integer in Set Type-math.jpg

    Hai.. I need help to solve this question.
    I just dont understand what is the meaning by the greatest integer in the form of sets.
    for example (a);
    f-1=(B)

    B-1={0,1} . I get until this step. But how to solve it using the greatest integer @ floor of x?

    I also dont understand about the different between {} , [ ], and( ) .

    Thanks for the help.
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  2. #2
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    Re: Greatest Integer in Set Type

    Quote Originally Posted by aquhzie02 View Post
    Click image for larger version. 

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    Hai.. I need help to solve this question.
    I just dont understand what is the meaning by the greatest integer in the form of sets.
    for example (a);
    f-1=(B)
    B-1={0,1} . I get until this step. But how to solve it using the greatest integer @ floor of x?
    I also dont understand about the different between {} , [ ], and( ) .
    It seems that you really need instruction in basic interval notation.
    There are four types of finite intervals:
    1. closed, $[a,b]=\{x: a\le x\le b\}$
    2. open $(a,b)=\{x: a< x< b\}$
    3. $(a,b]=\{x: a< x\le b\}$
    4. $[a,b)=\{x: a\le x< b\}$


    1. $f([0,2]) = \left\lfloor {[0,2]} \right\rfloor = \left\{ {0,1,2} \right\}$
    2. $f((0,2)) = \left\lfloor {[0,2)} \right\rfloor = \left\{ {0,1} \right\}$
    3. $f((0,2]) = \left\lfloor {[0,2]} \right\rfloor = \left\{ {0,1,2} \right\}$
    4. $f([0,2)) = \left\lfloor {[0,2)} \right\rfloor = \left\{ {0,1} \right\}$


    YOU must study both those lists until you completely understand the subtle differences.

    $f^{-1}(\{3,4\})=[3,5)$, $f^{-1}(\{1,2,3,4\})=[1,5)$, $f^{-1}(\{4\})=[4,5)$

    Note that $f([2,3])=\{2,3\}$ BUT $f^{-1}(\{2,3\})=[2,4)$.

    P.S. Parts (c) through (f) have no answer. The reason being that the $B$ sets in those parts are not subsets of the range of $f$.
    Last edited by Plato; Mar 18th 2017 at 02:22 PM.
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