That shows how many unique addresses are used each day. Not how many there are in existence (or "seen"  on the network) in total. Is there another source?

Is there a way to see how many addresses there are in existence today? (or an approximation)

Bitcoin.it claims it would take an attacker 2^107 more time to create a collision than a valid block. How is this number calculated? It must be a ratio between number of tries for a collision and number of tries for a valid block is created. 

The transaction fees will be a reason to continue. But I don't know if this will attract a large group of miners (at least not as many as now). And if that is the case, the computing power on the network* will decrease, making an attack (fraud) more likely.

I was thinking about the incentives for miners. Now there are two incentives:a reward in newly created bitcoins and a (smaller amount) of transaction fees. At the time no new bitcoins will be created, and the fees are the only incentive, I guess it will be less motivating for people to mine. Which leads to (much) less computing power on the network and an increased likelihood of someone frauding the chain. What do you guys think of this?

Thanks. In that sense I can't think of it either.

A short question for which I didn't find an answer: is recursion possible in the scripting language that Bitcoin uses?

Thank you, makes sense! Why did it take 2^32 attempts with difficulty 1? I know Bitcoin works with a target hash and SHA-256. There must be a (complete) way to calculate the average number of hashes required with a certain target. Anyone can help me with this?

I used the search function but didn't find an answer.

I did read about difficulty on https://en.bitcoin.it/wiki/Difficulty, but the number still doesn't make sense to me. Can anyone explain me what this number means and how to use it?

Doh, of course! Thanks a lot for clearing up! 

Thank you for all the replies.

So if I get it right now, a recipient who want to keep his anonymity does the following:

1. Send his bitcoin address only to the sender, for example via https. Only the sender knows the address is coming from an identity now and nobody else knows about the connection between the address and the company/person behind it.
2. Automatically generates a new bitcoin address for every transaction.

My last question, I guess, concerns point 1. Am I right this can be done using public-key cryptography? Let's say Alice wants to pay Bob for a product. She sends her request to Bob. Bob then encrypts his (new) bitcoin address with Alice's public key. This way only Alice can decrypt his message and see Bob's  bitcoin address. Alice then transfers her bitcoins to Bob's address. This way nobody else could have seen Bob announcing his bitcoin address. Is this the way it is usually done?

I do understand that I, the sender, remain anonymous.

What I do not fully understand is how a recipient can remain anonymous. I mean, every recipient has to send his public address to the sender, right? And businesses have to "announce" this on their website. So if you would keep track of the addresses that, let's say WordPress, announces on it's website for senders to send their bitcoins to, you can see which transactions are going to WordPress. Everybody could see the incoming cashflow of WordPress. Am I wrong?

Dear bitcointalkers,

This is my first post and question here. I have read the introduction and several other pages about bitcoin, but I don't understand the anonymity of Bitcoin transactions yet. I see it as follows:

1. I want to send a sum of bitcoins to a guy for that will make a website for me
2. My address is public (public key) and his address is publicly known (on the website he has his bitcoin address, let's say he uses one)
3. I send my bitcoins to his address (I do understand here how a digital signature works, more or less)

Now, all transactions are public and registered in the blockchain right?  So anybody who knows this guy's public bitcoin address (and everybody can know this because it's on his website) can see how much bitcoins he got from me. Besides, his name is on his website. I don't have my name and address posted anywhere so I remain anonymous. I suppose I don't really understand, but where is the anonymity for the guy/shop delivering the service here?