The woman utters this phrase to show that even if she dies, she would die as a martyr and her fight would not end.
This novel is set in a hypothetical futuristic society. In this society, books have been forbidden and any book found by authorities is immediately destroyed.
In the first part of the book, an old woman decides to stay and burn with her books when authorities arrive, and before she dies she says:
This phrase is a quote from Hugh Latimer who said these words before being burned for heresy. This implies the woman wants to show she will not live without her books and even if she dies with them she is a martyr and her fight for knowledge and freedom stills continue.
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Fahrenheit 451 by Ray Bradbury
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