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Except that any secure digital cash system must have the property that I mentioned -- the tokens must grow with the number of transactions:
I'm not sure if "token" is a valid concept in bitcoin. There are just practically unlimited number of "accounts" which each hold a variable amount of bitcoins. Also, there is a central authority of sorts for bitcoin, which is the public blockchain that stores all the transactions in bitcoin network, and makes it possible to know the value of every account. That transaction record is managed in a peer to peer fashion.
So tokens don't grow since there are no tokens to begin with.
I think BitCoin is a great concept
Except that decentralized digital cash is inherently flawed, since the tokens will always grow linearly in the number of transactions they are used for. In other digital cash systems, this problem is solved by having an issuing authority (bank, government, etc.) that accepts old tokens and issues fresh tokens. In the case of Bitcoin, no such authority exists, so the tokens are just going to keep getting bigger, and eventually they will be too large to be useful.
What? I think you may have misunderstood some aspects of Bitcoin. You can easily divide and combine bitcoins in any way you want. You can combine one thousand 0.001 bitcoins to a single bitcoin, or do the same in reverse and divide. The smallest possible unit is 0.00000001 BTC.
Bitcoin is not perfect, but this is NOT one of it's problems.
Site uses only CPU mining, and I can guarantee you that you will be spending more on electricity than gaining in bitcoins with the current valuation. You need a powerful GPU or some other specialized hardware to do it profitably. It's cheaper and easier to just buy bitcoins.
That said, if it works as a steppingstone for you to get interested in Bitcoin, and actually familiarize yourself with the system, before coming to the wrong conclusion about its validity, then go for it.
Here are some places you can start with:
http://www.bitcoin.org/bitcoin.pdf for the original whitepaper that everything is based on (internalize this)
https://en.bitcoin.it/wiki/Myths for some of the more common myths flying around about bitcoins
https://en.bitcoin.it/wiki/Weaknesses for some ACTUAL weaknesses in the system, so you don't have to come up with the same old false ones that come up with these thread all the time.