Quote from: threeip on July 02, 2013, 12:11:49 AM

The pub is derived from the priv, so if you had the pub you would also have the priv.

More than one private key can technically result in the same bitcoin address.

Therefore, if you have the same private key then you have the same address, but if you have the same address, you don't necessarily have the same private key.

Quote from: elements on July 02, 2013, 12:12:27 AM

In other words if Alice has a wallet that contains the address xyz and Bob has a wallet that contains the same address xyz
both have the same private key?

(And thus all individual addresses of Alice and Bob can be signed with their own or the other one's private key?)

Not necessarily, but they both have a private key that will create a valid signature for spending bitcoins that are associated with address xyz. Not all individual addresses, only address xyz.

Quote from: elements on July 02, 2013, 12:13:41 AM

ok, so having the same adress means actually the same private key.

That makes sense.

Thank you!

No, having the same private key means having the same address. Having the the same address does not necessarily mean having the same private key, but as long as you have a private key that is a valid private key for the address you are able to spend the bitcoins at that address.