Well, yes and no. Bitcoin is dependent upon electricity in the same sense that your lights are, you may not be able to use them when the power is out, but they work again as soon as the power is back on. Actually, though, I have my bitcoin on my android phone, so I can actually transact (with others with android phones) during a power outage also. This method isn't easy or simple, but it is possible. Physical bitcoin tokens also exist, if physical things are all you trust.
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