Newbie Here (Question about "Backing Up")

[New_Frontier]

I'm still trying to wrap my head around this whole BTC thing but I'm a strong believer in its long term validity, use, & the need of a digital currency.  I have a question about backing up my BTC coins. 

Please correct my logic if I'm not understanding this correctly. 

I purchase 5 bitcoins from MTGox
I then download the application BTC Wallet (Bitcoin-QT)
Then click on "Received" icon in Bitcoin-QT and copy the address shown (This is your new personal BTC address you will use to RECEIVE BTC from people, banks, websites, etc.)
I then go back to MTGox and using my new BTC receive address I do a WITHDRAWAL of all my Bitcoins & send them to new BTC address
Once the coins get received into my wallet I then backup the wallet application. thus "theoretically" at this point my coins are safe and can never be stolen or spent without me.  (I understand someone can steal the coins in the wallet by hacking my computer, viruses, etc.)

Question: Is my path of logic incorrect?  Do I have a general grasp of how this works?  Should I be doing something different to secure my coins? 

Thank you all for your time & responses I truly appreciate it.     

[UnseenUnheard]

I recommend the Bitcoin wallet Electrum. Its simple, clean, and has a built in pass-code failsafe in case you ever forget your password. http://electrum.org/

[steveioio]

I think yes you have it. I would however encourage you to try the whole process with 0.01 BTC a few times to make sure everything is working OK and you can get your 0.01 BTC back into mtgox and it is accepted.

[DannyHamilton]

Bitcoin-Qt is one possible wallet program you could choose.  Make sure you understand what you are choosing before you choose a wallet program.  Each has it's own "quirks", and depending on your use, technical skill, and personal security habits, some wallets might be better suited for you than others.  Some of the more popular wallets to investigate before making your decision:

Paper Wallets (or other offline storage of private keys)
Armory
Bitcoin-Qt
Electrum
MultiBit
https://blockchain.info/wallet

Your general grasp is correct.

You use a wallet to generate bitcoin addresses. A wallet can have multiple addresses. You can have a separate address for every sender, or even the recommended separate address for every transaction.

Your wallet keeps track of the private keys needed to send those bitcoins elsewhere in the future.

Some wallets (such as Electrum) only need to be backed up once.  The entire wallet can be rebuilt from the seed value contained in the backup.
Other wallets (such as Bitcoin-Qt) need to be backed up on a regular basis.  The wallet randomly generates a new address that it doesn't tell you about every time you send bitcoins.  The backup only has the next 100 addresses that will be used.

If anyone gains access to an unencrypted copy of your backup (virus, trojan, hacker, nosy roommate, etc), they can take/spend your bitcoins, so protect your wallet and backups carefully.

If you permanently lose your wallet and all backups (flood, fire, tornado, forgot password, etc), you will never again be able to access those bitcoins.  There is no way to recover them if the private keys stored in the wallet and backups are lost.

[New_Frontier]

Thank you all for your responses they were very informative & hopefully will help others with similar questions. 

What stops people from just generating these long numbers & calling them Bitcoins & trying to sell & spend them? 

[rmbc]

It's all signed and counter-signed and counter-counter-signed etc with cryptographic functions and it's part of one huge "chain", acting as some kind of a general ledger, where each block and each transaction in each block is signed such and so.

You can generate any transaction you want, but as long the (heavily signed) blockchain doesn't agree with you that the coins in that transaction exist and you own them, noone else will accept them as such.

the cryptographic functions behind it are so far unbroken. I'm told the math behind is is beautiful
trying to break those with the only known method (brute force) with current computing power would take more time than the universe has existed so far.
building a (conventional) computer to crack it fast enough would require more matter than the earth contains.

[DannyHamilton]

Thank you all for your responses they were very informative & hopefully will help others with similar questions. 

What stops people from just generating these long numbers & calling them Bitcoins & trying to sell & spend them? 

The "long numbers" are not bitcoins.  They are the private keys that allow you to broadcast a signature that informs the entire network that you are turning over control of some bitcoins to someone else.  There is nothing you can point to and say "that's a bitcoin".  The term "a bitcoin" is an abstraction that we humans use to make it easier to discuss the exchange of value that occurs with transactions.

All the value is represented in the public blockchain that everyone has a copy of.  When you "send a bitcoin" what you are actually doing is adding an entry to this public ledger that says that a previously received value (that the entire network can see in the blockchain was actually sent to your address) is being reassigned to some other bitcoin address.  Your private key is mathematically connected to your bitcoin address in such a way that a signature generated with that private key can be proven to have been made with the private key for that address.  So the entire network verifies that the signature provided is valid before is reassigns the value to the new address.

Anyone who knows your private key can create the signature which allows them to take/spend all value associated with the bitcoin address that was generated from the private key.  Without that private key, it is impossible to create a signature that the network will accept.

[New_Frontier]

Thanks guys for all that good info.  I appreciate the informative responses & how helpful the community has been to "newbies".  You guys Rock!

[MouseTrap]

I dont get the cold wallet process, would rly like a newbie guide for this.