What if you run a full bitcoin node and your node software is Bitcoin core QT which has a native wallet you are essentially then self hosting your own wallet.
self-hosted wallet is a play on words. there is no wallet. you control the private key or you don't. you don't need bitcoin core or a computer to have custody of your private key. the private key could be stored in your head as a simple poem.
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Yeah but you need some kind of tool to actually create the private keys from the seed phrase, and that's part of a wallet.
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correct. the generation tool is usually bundled in.
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What should you call hardware wallets then?
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Calculators
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Hardware keys
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