"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.
At my school, they said "one-to-one" and "onto" for "injective" and "surjective". But then, the linear professor started teaching the subject in 1952, so he was quirky.
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.