These terms are used to indicate the general trend of the graph, whether it’s going up or down. They are named after these animals because of the ways they attack their opponents. A bull thrusts its horns up into the air, while a bear swipes its paws downward. So these animals are metaphors for the movement of a market: If the trend is up, it’s a bull market. But if the trend is down, it’s a bear market.

After the miner has successfully verified that all transaction in the block are valid, he must then compute a cryptographic hash. It is necessary for miners perform this computation in-order to prevent just anyone from being able to create blocks therefore secures the network against fraudulent blocks. Computing a cryptographic hash requires a large amount of computing power as hundreds of millions of calculations are needed to be performed each second. This process is known as proof-of-work. Once the miner successfully solves the hash, his block is then relayed to the network to be checked against the consensus rules. Once accepted, the block is then added to the blockchain network and the miner is rewarded with set amount of the cryptocurrency.
Let's say you had one legit $20 and one really good photocopy of that same $20. If someone were to try to spend both the real bill and the fake one, someone who took the trouble of looking at both of the bills' serial numbers would see that they were the same number, and thus one of them had to be false. What a Bitcoin miner does is analogous to that--they check transactions to make sure that users have not illegitimately tried to spend the same Bitcoin twice. This isn't a perfect analogy--we'll explain in more detail below.
The bitcoins can also be stored in online wallets. There are specialized websites that offer bitcoin wallet services. However due to these sites being a frequent target for hackers, keeping bitcoins in online wallets is not recommended when you can easily store them offline on your computer. Wallets can be useful for storing small sums of bitcoins so that you can make quick online purchases. Some of the more popular wallet services are Blockchain and CoinKite.
Bitcoin solves the so called ‘’double spending problem’’ present with digital goods. For example, if I have an mp3 file or an ebook on my computer, I can freely copy that file a thousand times and send it to a thousand different people. For a digital currency, the possibility for unlimited copying would mean a quick hyperinflationary death. Bitcoin solves this by maintaining a peer to peer network and recording each transaction in a public ledger called the block chain. Say I send 1 bitcoin from my bitcoin address to my friend John. The bitcoin network records that transaction in the block chain and I no longer have possession of that bitcoin. The coin ‘’moved’’ from my bitcoin wallet to John’s wallet.
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