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Not for the first time in literature and society, and assuredly not for the last, there is one set of standards to which Penelope must adhere, and a very much looser set for Odysseus. And yet, in some ways, Odysseus does remain faithful to his wife. He shares another woman’s bed, but he doesn’t share her idea of their future. She offers him something of enormous value–immortality, for which all heroes strive, one way or another–and he rejects it. He would rather return to his less beautiful, mortal wife. Homeric heroes make huge sacrifices for even a brush of immortality: Achilles specifically chooses a short, glorious life that will result in fame which outlives him (a kind of immortality) rather than a longer, less famous existence. And here is Odysseus, offered eternal life but rejecting it. And all for the chance to return to a woman he has not seen for twenty years. A divorce lawyer might not call this fidelity, but it is something.
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