Show that if x is a real number, then if x is not an integer and if x is an integer.
Step1:
In this problem we need to show that
, if x is not an integer
And
, if x is an integer.
NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing.
Example :

Step2:
Case(1): If x is not an integer.
Let us consider , , where a is an integer and .
Then ,
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