what does function symbol $f:\mathbb R\to\mathbb Z$ means? I have just started learning functions. 
I am troubled by this:   $f:\mathbb R\to\mathbb Z$ where $\mathbb R$ represents the set of real numbers and $\mathbb Z$ represents the set of integers. 

What does this statement mean when it is mentioned infant of a function such as $f:\mathbb R\to\mathbb Z$ where $f(x)=\lceil x\rceil$. 

Thank you!
 A: What it means is it takes a real number as an input value ($x$) and outputs or maps to a integral value
For example, f(2.5) = 3, f(2.4) = 3, f(2) = 2. All the values between the parentheses are the inputs or $x$ values and must be a real number. The values after the equal are the out puts, which are and must be integers.
A: For any sets $X$ and $Y$, the notation $f:X\to Y$ means that $f$ is a function that takes as input elements of $X$, and gives as output values of $Y$.
In your case, $\Bbb R$ and $\Bbb Z$ are sets, so when we write $f:\Bbb R\to \Bbb Z$, we mean that $f$ is a function that takes any real number as input, and gives out an integer as output.
A: In the context of functions the statement $f:A\to B$ means exactly that:


*

*$f\subseteq A\times B$

*For every $a\in A$ there is a unique $b\in B$ such that $\langle a,b\rangle\in f$


If $f:\mathbb R\to\mathbb Z$ denotes a function then the statement $f(x)=\lceil x\rceil$ means exactly that: $$f=\{\langle x,\lceil x\rceil\rangle\mid x\in\mathbb R\}$$
