I' ll take bitcoin as an example.
Is it mandatory that the value of all bitcoins is equal to the value of the world economy?
Can this value be archived before all the bitcoins are mined?
When I buy bitcoin someone will take my dollars.
So how can we technically replace all dollars with the bitcoins?
In the end will there always be someone with only dollars in their pockets or am i wrong?
Your example is flawed because not even the dollar represents the whole world economy there are many other currencies that are very strong, what I think it is going to happen is that bitcoin is going to become one of the strongest currencies of the world and a significant amount of trade is going to move through it, it is not going to become the first world currency because governments are never going to allow that.