Explaining discontinuity in a greatest integer function

[Deathfish]

Homework Statement
Find the numbers, if any, where the function is discontinuous.

f(x) = [[x - 2]]

The attempt at a solution

function is discontinuous for all integer values of x.

I know that this is the obvious answer, however I am required to explain this in clear mathematical style, methodically explaining why this is so. Also I am not sure if this is the correct notation for presenting the answer. Anyone can help me out?

 

[micromass]

Hi Deathfish!

There are several (equivalent) ways to show continuity/discontinuity. Which ones have you seen and which do you prefer?