Comparing the real (integer part) of a number.

[mtayab1994]

Homework Statement

Compare between E(x+y) and E(x)+E(y) for every real number x and y.

E() refers to the real integer part of the number.

The Attempt at a Solution

Well I know that we have to split it up into 3 cases. One for which both are positive, both negative, and one of them is negative. For example I know when we have x and y greater than 0 we get E(x+y)≥E(x)+E(y) because let's take x=1.5 and y=1.6 then E(1.5+1.6)= 3 and
E(1.5)+E(1.6)= 2. Can anyone help me come up with a proof for this?

 

[mtayab1994]

Anyone have any ideas.

 

[Mark44]

See http://en.wikipedia.org/wiki/Floor_and_ceiling_functions, especially the part about the floor function (also known as the greatest integer function).

 

[mtayab1994]

Alright Thank You I came up with a proof from what i read on wiki.