For which real numbers x and y is it true that ⌈x +y⌉ = ⌈ x⌉ +⌊ y ⌋
Solution
Step 1:
In this problem we need to show that
is true for all real numbers x and y.
NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing.
Example :

Given: x and y are real numbers.
Let us consider , and where a , b are integers and are real numbers such that .
So ,
Now
, since
, since a , b are integers.
Therefore ,
................(1)