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One important symbol is that of the title itself: Fahrenheit 451 is intended to refer to the temperature at which paper catches fire (although this is up for debate; different papers ignite at different temperatures). It occurs three times in the novel, twice when Montag is burning something, once when he tries to impress Clarisse with the power of his job. One meaning of the numbers is that the government, in annexing "firemen" to serve their own purposes, have no shame in showing citizens exactly how they are controlled.
Another important symbol is, of course, fire. This shows throughout the novel, acting in many important scenes, and fire imagery shows up even when there is no fire present:
People were more often -- he searched for a simile, found one in his work-torches, blazing away until they whiffed out.
(Bradbury, Fahrenheit 451, Google Books)
Fire, which can burn long or short, is very symbolic of the culture; life is worthless, and people risk their own and kill others without concern: "snuffing life's flame." Also, the duration of a fire depends on fuel; without the mental "fuel" of books, people's lives burn fast and burn out, stopping either in mental stagnation, such as Mildred, or in death, such as the many teenagers who race their cars at deadly speeds. Montag burns books for the government, but by igniting real flames, he is extinguishing the mental flames of reading and knowledge.
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