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In 1971 the US Treasury stopped backing US Dollars with gold (see HowStuffWorks.com), but this did not devalue the dollar. Currencies derive their value based on how difficult they are to obtain. Bitcoins are valuable because they are limited, and they can only be generated through a slow computational process. It takes time, electricity and computers to generate bitcoins.
Actually, Bitcoins are valuable because there are people who accept Bitcoin for payment, i.e. they can be exchanged for other things of value. The limitedness of Bitcoins just helps keep that value.
