A wallet stores the information necessary to transact bitcoins. While wallets are often described as a place to hold[88] or store bitcoins,[89] due to the nature of the system, bitcoins are inseparable from the blockchain transaction ledger. A better way to describe a wallet is something that "stores the digital credentials for your bitcoin holdings"[89] and allows one to access (and spend) them. Bitcoin uses public-key cryptography, in which two cryptographic keys, one public and one private, are generated.[90] At its most basic, a wallet is a collection of these keys.

“Most enforcement actions are kept confidential until they’re resolved to protect both the defendant (from bad press) & the government (from losses & inconsistencies). That’s why this case was settled before it was announced. On that point, remember all those subpoenas the SEC sent out earlier this year? Just because you haven’t heard about them recently doesn’t mean there aren’t dozens of investigations going on behind the scenes. Sooner or later, the floodgates will open,” Chervinsky said.
The simple answer is: just like physical currency exchanges. You're essentially buying one currency with another. The relative value of a nation's physical currency is a reflection of the country's economic and financial health, especially since we moved off of the gold standard. The U.S. dollar, for example, is worth more than that of the Mexican peso due to the discrepancies between the two countries' economies—therefore you can buy lots of pesos for very few dollars (the dollars being relatively more valuable).
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Transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin was invented by an unknown person or group of people using the name Satoshi Nakamoto[9] and released as open-source software in 2009.[10] Bitcoins are created as a reward for a process known as mining. They can be exchanged for other currencies,[11] products, and services. Research produced by the University of Cambridge estimates that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet, most of them using bitcoin.[12]
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