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Whether the term is offensive or not is open to debate. Japanese has several cases of using gai (外) (outside) plus a noun to indicate one of `noun' from another country. For example gaisha (外車) for foreign cars, or gaika (外貨) for foreign currencies.
Some people are deeply offended by the word, saying that gaijin refers to outsiders rife with undesirable characteristics. There is no doubt that is one meaning of the word.
Gaijin is also used in many cases where it is probably not intended as a negative statement. Consider that it is common in the Japanese language to address people whose names are not known, or even if names are known, by titles: omawari san, Mr Policeman; sushiya san, Mr Sushi Shop. It is not unusual for a Japanese speaker to call a non Japanese who is otherwise not known, gaijin san.
Gaijin appears in some early Japanese literature such as the Heike monogatari meaning "outsider" or "enemy".