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I'm using the mobile "trust wallet" app, and my plan is (was?) to write down the mnemonic key and keep it in a safe place, then delete the app.

Then whenever I need to receive or send money to a petty cash address, take my paper mnemonic from my safe place and import it on trust wallet.

Now, from what I saw online (source: https://www.youtube.com/watch?v=A5I55aOgX2o at around 4:00) it appears that keeping the private key in paper is dangerous because of the way bitcoin works with change and other technicalities, I could lose my btc (even without losing the paper wallet), and I can't really understand why... Can anyone please help me shed some light here?

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There is a difference between a traditional paperwallet and a BIP32/39 based mnemonic and seed system.

Traditionally, a paper wallet would be for a single address, with a single private key. When importing this into another wallet, a possible concern was that the change from any transaction would not be returned to that single address, but instead be sent to another address belonging solely to that online wallet.

This is easily solved by using a wallet such as electrum, which ensures that change is sent back to the single address, since any wallet you create will have just that one address in it.

If you import that address into a preexisting wallet, then you need to build a transaction that returns the change to that address.

With BIP32/39, the seed is imported as a whole - this results in adding not just one address, but the entire address chain. As a result, any change will return either to the sending address, or to another address controlled by your mnemonic. This is considerably safer, and better for privacy.

Naturally, this also means that if your mnemonic is compromised, all of your addresses are compromised.

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