"one to one" typically means injective (into). That is, every element in the image corresponds to a unique element from the domain. That's just a convention,

"one to one" typically means injective (into). That is, every element in the image corresponds to a unique element from the domain. That's just a convention, though. To be precise one ought to use terms like injection, surjection, and bijection. When speaking informally, sometimes people say "one to one" and mean bijection. It's a catch 22 in a way, because you can only divine the precise meaning if you already understand the proof, viz., Cantor's proof isabouf bijections sp "one to one" means that.