The actual truth is even weirder: if Bitcoin takes over as the world currency, its value in $USD will be infinite, but the question will be meaningless, as the dollar will be worthless. Currencies tend to be winner-take-all within a society; if one takes over, its rivals lose all value, as their only value is in being a medium of exchange and store of value.
This is perhaps a contributory factor to the Bitcoin's volatility: if you actually believe it's going to succeed, unambiguously, the rational thing to do is to move all your wealth to Bitcoin. And similarly, if you believe it's going to fail, the currency by definition is worthless.