Which part? One-to-one means that there's an unique element in the range for every element in the domain. That doesn't mean there are the same number of element

Which part? One-to-one means that there's an unique element in the range for every element in the domain. That doesn't mean there are the same number of elements. (EDIT: typo strike second range, replace with domain!) (EDIT2: To reply to a reply below: it's absolutely trivial to provide the function: to prove it's true wouldn't be, at least set theoretically, which is how I'd do it.)