Problem 23E
Prove that if m is an integer, then ⌊x⌋ +⌊m − x⌋ = m − 1unless x is an integer, in which case, it equals m.
Solution:
Step 1:
In this problem we need to prove that if m is an integer , then
unless x is an integer , in which case , it equals to m.
NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing.
Example :
Example : {2.3} = 0.3

Case(1): If x is not an integer , then
.
Therefore , if x is not an integer then