Can two distinct formulae (or series of formulae) have the same Gödel number? As I am studying Gödel's incompleteness theorem I am wondering if two distinct formulae or series of formulae can have the same Gödel number? Or the function mapping each formula or series of formulae to a Gödel number is not invertible?

Two different formulas, or strings of formulas, cannot have the same index (Gödel number). 
In the usual indexing schemes, not every natural number is an index. So the function is one to one but not onto.
