What does this mean? (typing)

Question

anonymous · Answer

$$\forall y \in Y, f ^{-1} ( \left\{ y \right\} )$$ contains at most one element.

hartnn · Answer

For all elements y, that belongs to set Y, the inverse function of y f^-1
contains either 0 elements or 1 elements

anonymous · Answer

The main thing that I don't understand is what does the {y} inside the f^-1 mean. Is it set builder notation inside the function or what? Why is there these kind {} or brackets?

anonymous · Answer

If it's any help this is for my Analysis class.

anonymous · Answer

So f takes a set as an input and outputs a set?

hartnn · Answer

even i think that y is not just an element, it takes set of elements as input

anonymous · Answer

I think I realized something. Is it just a really complicated of saying it's a bijection?

anonymous · Answer

It could be, assuming those {   }  don't mean much.

anonymous · Answer

Actually I'm starting to think it's actually a complicated way of saying one to one.

anonymous · Answer

If it were one to one, shouldn't it be exactly 1 element?

anonymous · Answer

So maybe injective?

anonymous · Answer

It wouldn't have to have an element if it's one to one
The drawing is a one to one but the one I circled wouldn't have an element.|dw:1349154799159:dw|
Also, isn't injective and one to one the same thing?