I'm not sure late unification is necessarily the determing factor here. e.g. look at Italy
so sexy
something so sexy needs to be marked as NSFW
you can model the tax on the supply or the demand. in most simple models the outcome is the same
technically yes, but the proof would usually show that this works by constructing the bijection of [0,1] and (0,1) and then you'd say the cardinalities are the same by the Schröder-Berstein theorem, because the proof of the latter is likely not something you want to demonstrate every day
even if that's not how you can write it, one gets the same issue in yours subtracting infinity from both sides
it's actually Vulcan
ah, but don't forget to prove that the cardinality of [0,1] is that same as that of (0,1) on the way!
no, there aren't enough integers to map onto the interval (0,1).
probably the most famous proof for this is Cantor's diagonalisation argument. though as it usually shows how the cardinality of the naturals is small than this interval, you'll also need to prove that the cardinality of the integers is the same as that of the naturals too (which is usually seen when you go about constructing the set of integers to begin with)
actually you can for each real number you can exhaustively map a uninque number from the interval (0,1) onto it. (there are many such examples, you can find one way by playing around with the function tanx)
this means these two sets are of the same size by the mathematical definition of cardinality :)
I'm pretty sure he was involved with the liberation theology movements in Argentina before the previous pope clamped down on it (in his capacity as a cardinal)