find the limit

[spacewater]

\(\displaystyle \frac {lim} { x->3} (2-[[x]])\) (find the limit of 2-[[x]] as x approaches 3)

What do I have to do with \(\displaystyle [[x]]\)?
There is a very brief explanation on step function in my text but I am unable to comprehend it.. can someone explain to me please?

 

[BigGlenntheHeavy]

Is [[x]] the greatest integer function?

 

[spacewater]

Ah yes

 

[BigGlenntheHeavy]

\(\displaystyle [[x]] \ = \ greatest \ integer \ n \ such \ that \ n \ \le \ x.\)

\(\displaystyle Ergo, \ \lim_{x\to3^{+}} (2-[[x]]) \ = \ (2-3) \ = \ -1\)

\(\displaystyle \lim_{x\to3^{-}} (2-[[x]]) \ = \ (2-2) \ = \ 0\)

\(\displaystyle Hence, \ \lim_{x\to3} \ (2-[[x]]) \ does \ not \ exist.\)