even if that’s not how you can write it, one gets the same issue in yours subtracting infinity from both sides
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 :)
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)
I like my potatoes raw thank you very much
every dollar you raise, the fewer customers you get. the point is that you should want to raise the price whenever the relative drop in customers is less than the relative increase in price to maximise profits (where marginal cost is marginal benefit :) )
Right, and this Walmart in Europe would be where exactly?
I think the worry is a WW3 with China
you don’t need to say yes if someone asks you?
XMPP?
won’t they just be more reliant on lobbying gifts to compensate?
while the last point is perhaps the main determinant theory behind why many older people are not being owing more right wing, I’m a little confused by your first two points.
especially the fact that people have greater access to knowledge and are forced to think more critically. if anything, with the advent of the internet, echo chambers have never been easier, preventing critical thinking. this leads to a growing of extreme positions which further reinforces such views due to tribalistic fallacies in our thinking and the need for these tribal identities to distinguish themselves.
can’t you just buy a cheaper USB 3.0 speed cable anyway? or is this a hardware limitation that Apple have put in the port of the phone?
Removed by mod
look at mr big spoon here
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