Is this a valid function? I am stuck with the question below, 
Say whether the given function is one to one. $A=\mathbb{Z}$, $B=\mathbb{Z}\times\mathbb{Z}$, $f(a)=(a,a+1)$
I am a bit confused about $f(a)=(a,a+1)$, there are two outputs $(a,a+1)$ for a single input $a$ which is against the definition of a function. Please help me out by expressing your review about the question. Thanks

If $f\colon A\to B$, then the inputs of $f$ are elements of $A$, and the outputs of $f$ are elements of $B$, whatever the elements of $B$ may be.
If the elements of $B$ are sets with 17 elements each, then the outputs of the function will be sets with 17 elements each. If the elements of $B$ are books, then the output will be books.
Here, the set $B$ is the set whose elements are ordered pairs. So every output of $f$ must be an ordered pair. This is a single item, the pair (just like your address may consist of many words and numbers, but it's still a single address).
By the way: whether the function is one-to-one or not is immaterial here (and it seems to me, immaterial to your confusion...)
