What is a surjective function? I am a 9th grader self-studying about set theory and functions. I understood most basic concepts, but I didn't understand what is a surjective function. I have understood what is an injective function, and if I know what is a surjective function, I think I could understand what is a bijective function (this is my main goal).
In formal terms a function $f$ from $A$ to $B$ is said to be surjective if for all $y$ in $B$, there exists $x$ in $A$ such that $f(x)=y$. I don't understand this clearly because i'm still new to these notations. Can you explain this in intuitive way? And for example can you give me a surjective function that is not injective, and inversely, and neither one of the two?

$f\colon A\to B$ is surjective if every element $b\in B$ has a pre-image in $A$. In other words: the equation $\;f(x)=b \enspace(x\in A)$ always has a solution, whatever the value of $b$.
