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My question is 2 part:
1. How does somebody know that a set of bitcoins is lost? Merely declaring that I've lost my private key and hence bitcoin makes the coins lost?
2. What impact(and why?) would be on the price of bitcoin if I lose a huge amount of bitcoin today? Say 1 billion?

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  1. Yes, pretty much the only way to know coins are lost is through someone making the information public by declaring they no longer have access to the private key. Otherwise they would just look like someone who hasn't moved their coins if viewed on the blockchain.

  2. There's actually a limit at the current moment of 21 million bitcoins. So technically losing 1 billion bitcoins is not possible since it's larger than the limit. But taking on the spirit of the question, If someone was to lose a large amount of bitcoin theoretically it should make the rest of the coins more valuable. In practice though I'm not sure it always works this way since in your first question we brought up the notion that confirming lost bitcoin is not easy.

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