Determine whether the following function is (a) injective and (b) surjective the function is as follows: $f:\mathbb{R} \rightarrow \mathbb{Z}$ defined by $f(x) =$ the least integer greater than or equal to $x$.
here is what I have for the proof of injective:
Suppose $f(x)=f(y)$ that is,
the least integer $\geq x =$ the least integer $\geq y$
I thought that this pretty obviously implied that $x=y$.
I am unsure as to how to begin the proof of surjective. 
Can someone help?

The function in question is known as the ceiling function $f(x)=\lceil x \rceil$.
To show that it is not injective, a single counterexample will do:
$$f(1.1)=f(1.3)=2\text{ and }1.1\ne1.3$$
To show that the function is surjective take $f(x)=n$ for an arbitrary $n\in\mathbb{Z}$. Then we can take $x_0=n$ (or $x_0=n-\frac{1}{2}$) so that $x_0\in\mathbb{R}$ and $f(x_0)=n$. 
