Exchange Transaction versus Blockchain Verification I am wondering about a question related to this post. According to bitcoinity, the number of bitcoin-trades at major exchanges per minute is roughly 400. However, as also pointed out by @eponymous in this answer, this number exceeds the trades which are verified on the bitcoin blockchain by far. However, how should I trust exchanges who do not provide real transactions in the sense that bitcoins are moved to my wallet? Is there a documentation on which exchanges provide this service and what exactly happens if I trade, say, USD versus BTC on a exchange which is not settling the trade on the blockchain?
If you send 0.1 bitcoin to an exchange, you would see it credited to your account, but that doesn't mean that it is in a wallet solely dedicated to your account. Instead, that 0.1 bitcoin is sent to a wallet which aggregates all transactions to the exchange.

When you withdraw the bitcoin, a transaction is published from the aggregating wallet to your supplied bitcoin address.

All internal movements are just crediting and bookkeeping to the internal systems of the exchange. This is the reason why it is generally not advised to keep bitcoin an an exchange for very long. If the company goes bankrupt or is hacked, you won't be able to retrieve your funds, because you don't have control over the wallet.