One of the properties of the floor function is this : $[x + y] = [x] + [y + x - [x]]$
Please let me know what the derivation of this property is...
Another question that I have is : What is the range of the floor function? Is it $\Bbb Z$, the set of all integers? Please let me know
And, I also have a little 'less mathematical question' : Is the derivation of properties of functions, like this one important to be known and there are about 10 properties of the floor function given in my textbook, do I have to learn each one of those? I mean will those properties be used in further concepts or are those just a one time thing?