could someone help me understand what is the meaning of the word "se" in this sentence?
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Literally it is one (se) + self (stesso), so it is often used just like that. Here are a few possibilities:
Cucino per me stesso/I cook for myself Lei compra il vestito per se stessa/She buys the dress for herself Abbiamo rispetto per noi stessi/We have respect for ourselves
According to my Italian-English dictionary if se (with an accent over the e) is placed in front of a pronoun such as lei it means self. ( It also depends on whether you can hear the speaker say it, as I could not hear it in this case. But I usually have trouble hearing/understanding her. )