Please, ask away, it's easier to clear up things when you have access to the experts, like on HN. If you purchase Bitcoin through an exchange, typically you do

Please, ask away, it's easier to clear up things when you have access to the experts, like on HN. If you purchase Bitcoin through an exchange, typically you don't have the private key, you just trust the exchange to do all the nitty gritty for you. If you generate a new address with a wallet software, it'll have a private key (that is much longer than the deliveryAddress.length) and you can move your funds from an exchange to this address (whereupon you'll have complete control). If you lose the private key it's [basically] impossible to recover with brute force, which is the point. If someone takes the physical hard disk from you and you have no backup of the info, yes, it's gone. If you somehow have your info stolen, but still remember it (via air-gapped pc text file or something) you can move the funds before they get swiped. Again, use wallet software to generate a new address with a new private key and repeat. So either you have a really good way to store your private addresses so you can still use your coins in the future, or you trust an exchange to hold the coins and you don't play in that realm at all. Those are the most popular options currently.