What does ceil mean ?

ceil(x) is the smallest integer which is greater than or equal to x. In particular, if x is an integer, then ceil(x) = x, and if x is not an integer, then ceil(x) > x.

 

Nope, read the defintion given above, then try again.

 

Yes, all 5.

 

Recall that

[tex]\begin{gathered}
\forall x \in \left( {a,a + 1} \right)\;{\text{where }}a \in \mathbb{Z}, \hfill \\
{\text{floor}}\left( x \right) = \left\lfloor x \right\rfloor = a \hfill \\
{\text{ceil}}\left( x \right) = \left\lceil x \right\rceil = a + 1 \hfill \\
\end{gathered} [/tex]

[tex]\forall x \in \mathbb{Z},\;\left\lfloor x \right\rfloor = \left\lceil x \right\rceil = x [/tex]