lemmington_steele

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 :)

well yeah, there's only so much sexy to go around. how else do you propose we save some for spiders?

you're assuming they're doing it by accident

yeah but by Cantor's diagonal argument, you still wouldn't be listing all the real numbers

assuming the interval includes all of the real numbers, then it is definitely larger than aleph null (the size of all countable infinities)

schwarzer Freitag, bitte