A "slice of life" is a category for a story that portrays a "cut-out" sequence of events in a character's life. It may or may not contain any real plot, and often has no exposition, action, conflict, or denouement, with an open ending. It usually tries to depict the every-day life of ordinary people. The term slice of life is actually a (more or less) dead metaphor: it often seems as if the author had taken a knife and cut out a slice of the lives of some characters, apparently not bothering at all where the cuts were made.
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