A wallet stores the information necessary to transact bitcoins. While wallets are often described as a place to hold or store bitcoins, 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" 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. At its most basic, a wallet is a collection of these keys.
Transactions are defined using a Forth-like scripting language.:ch. 5 Transactions consist of one or more inputs and one or more outputs. When a user sends bitcoins, the user designates each address and the amount of bitcoin being sent to that address in an output. To prevent double spending, each input must refer to a previous unspent output in the blockchain. The use of multiple inputs corresponds to the use of multiple coins in a cash transaction. Since transactions can have multiple outputs, users can send bitcoins to multiple recipients in one transaction. As in a cash transaction, the sum of inputs (coins used to pay) can exceed the intended sum of payments. In such a case, an additional output is used, returning the change back to the payer. Any input satoshis not accounted for in the transaction outputs become the transaction fee.
Bitcoin may react differently to inflation/deflation: Bitcoin differs significantly from fiat currencies, due to the fact that there is a limited number of bitcoins to be mined. Paper money, on the other hand, can be created at will out of thin air by central banks. Due to its limited supply, Bitcoin may potentially hold its value better than paper money, which can technically have an unlimited supply.
That constraint is what makes the problem more or less difficult. More leading zeroes means fewer possible solutions, and more time required to solve the problem. Every 2,016 blocks (roughly two weeks), that difficulty is reset. If it took miners less than 10 minutes on average to solve those 2,016 blocks, then the difficulty is automatically increased. If it took longer, then the difficulty is decreased.
Nakamoto is estimated to have mined one million bitcoins before disappearing in 2010, when he handed the network alert key and control of the code repository over to Gavin Andresen. Andresen later became lead developer at the Bitcoin Foundation. Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin.