The reference of "pajamas" in Boyne's work helps to bring out how Bruno sees the world. Normally, when we see pictures of Auschwitz and the Nazi death camps, the clothes that the victims are wearing would not be considered "pajamas." We would not use that term to describe what is being worn. Yet, Bruno's innocence and sense of naivete about the world and what is happening in it compels him to speak in an honest way, seeing the world in the most pure of terms. It is for this reason that he sees Shmuel wear "pajamas." Bruno sees what is happening through his own frame of reference. These "pajamas," of course, acquire greater significance as Bruno himself must don these clothes and wear them himself in order to honor the promise he made to Shmuel. In wearing the pajamas himself, Bruno is indistinguishable from the other victims of Auschwitz, looking the same as them and suffering the same fate even though he is German. The "pajamas" acquires much in way of significance for it is these clothes that Bruno wears in honor of a promise, and becomes the point of recognition in which we, as the reader, understand his heroism and his family, especially his father, understands the true horror of the Holocaust. For this reason, the pajamas is significant and bears relevance.
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