Did you know that, in colloquial speech, we use the infinitive to ask for permission or to offer something? The infinitive is often used with the Dative case.
1. (Мне) закрыть окно? Shall I shut the window?
2. Принести чаю? Would you like some tea? (Literally: “Shall I bring you tea?”)
3. Ему переписать рассказ? Shall he rewrite the story?
4. Нам не приезжать? Shall we not come?