# Thread: Greatest Integer in Set Type

1. ## Greatest Integer in Set Type

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.

2. ## Re: Greatest Integer in Set Type

Originally Posted by aquhzie02

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 $f$.