976
hmmmm
(mander.xyz)
Yes. Right under trolley. Will derail it.
Do we know if there's a track with a number of people tied down strictly in between the numbers of the two tracks?
Is every real number the smallest infinity? Would the infinity of every even number be smaller than the infinity of every integer? Or are they both aleph-null?
To elaborate on what Liz said, the way you compare sizes of infinite sets is by constructing functions between them. If you can place the items in the two sets in a one-to-one correspondence, the sets are the same size. If you try doing that between set A and set B, but there are elements in set A with no corresponding element in set B, then set A is bigger.
Cantor's diagonalization argument proves that there are more reals than integers. I found some explanations that aren't too jargony here. It's a great introduction to reasoning about infinities. If you're interested in the topic in general, I highly recommend Everything and More by David Foster Wallace, regardless of your level of math knowledge.
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Multi-track drifting. Also while some infinities are smaller if you're just counting out an infinite number of individual humans then I'm pretty sure they're the same size infinities one is just social distancing. Smaller infinities are ones like those in between each part of the bigger infinities. To represent a smaller infinity you'd maybe have to have an infinite number of smaller humans crammed into a spot the size of one of the spaces between the humans on the other track, or something along those lines. The real number track does contain smaller infinities between each integer via infinite decimal points but I don't think one track would technically be smaller than the other in this case since they run parallel to each other but neither are technically limited in the "length" of their infinity so to speak. But I could be misremembering how they classify smaller infinities.
Pull the switch as the trolley is on that rail so it gets stuck and the trolley kills nobody
this post was submitted on 27 Feb 2024
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