That's right.
Your wallet creates these addresses at random. These addresses do not exist anywhere in the blockchain or network until they are used for the first time.
You can even create these addresses on your own using dice, pen and paper.
Nobody assigns them to you. You create them.
In practice, it goes more or less like this:
1) Your wallet randomly chooses 24 words. These words act like a "seed" which generates a bunch of private keys.
2) These private keys are then used to generate public keys and addresses.
3) You can then share those addresses with anyone so they can send you money.
4) When someone sends money to one of your addresses, this transaction is registered into the blockchain (public ledger).
5) That money is now yours.
You might have several questions now:
QUESTION: If my addresses and keys are generated at random, what happens if another wallet generates my same keys and addresses? Wouldn't that person have access to my money?
ANSWER: Yes. They would be able to spend your money. However, the probability of this is so low, that it would take someone millions of years to generate your same keys using brute force.
The important thing here is that your keys are generated randomly. Your wallet needs to use enough entropy. A password "Iloveyoumom" is not as random as "dyb#$v72Df&z9wUmA".
Most wallets use algorithms that generate seeds pretty randomly. If you don't trust software for this, you can generate your own seed using dice.
QUESTION: How does the network knows that I'm the only one with permission to spend the money in those addresses? What happens if someone else tries to spend money from one of my addresses?
ANSWER: In order to spend money in Bitcoin, you need to sign the transaction using your private key. This digital signature proves that you have permission to spend the money in that address.
The network verifies this digital signature using your public key, but your private key remains private, it never leaves your phone or computer.
QUESTION: So let me get this straight. The wallet's main job is to generate keys and sign transactions?
ANSWER: That is correct. A wallet does not store money. It stores keys. Those keys are used to generate addresses and sign transactions.
QUESTION: So what is the difference between a warm wallet and a cold wallet?
ANSWER: A warm wallet stores your private keys on your phone or computer. This means that your keys are exposed to the internet and could potentially be stolen by a hacker.
A cold wallet stores your keys in an offline device. When you send a transaction, your cold wallet signs the transaction inside the device and then transfer this signed transaction to your computer or phone. This is done this way so that your private keys never leave your cold wallet device and therefore are never exposed to the internet.
QUESTION: Wow, so why would I want to use a warm wallet?
ANSWER: You use a warm wallet for everyday transactions and ease of use. The probability of being hacked is very low if you use an open source app such as Muun Wallet.
Use warm wallets for low amounts (less than $1k or so). Use cold wallets for life changing money or lifelong savings.
QUESTION: What happens if I lose my wallet?
ANSWER: You use your seed to restore it.
By the way, a cold wallet will never ask you to type your seed on a computer or phone. You type it directly on your cold wallet device. Remember, the seed of a cold wallet is never exposed to the internet.
QUESTION: What is the best way to store and protect my wallet seed?
ANSWER: Offline. Do not store your seed on your computer or phone. Never take a screenshot or a photo it either.
Keep it offline. Use pen and paper, tamper-evident bags, seedplates, etc. Keep 2 or 3 copies in different places. Hide them extremely well. Never tell anyone how much bitcoin you have.
QUESTION: I have my money on an exchange (Binance, Coinbase, Kraken, etc). What should I do?
ANSWER: You don't have any money. They own the private keys and therefore they own the money. Take your bitcoin off exchanges and move it into your own wallet before it's too late. Don't say we didn't warn you.
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