Fun fact: infinities can be different sizes, such that one infinity can be larger than another.
They’re still infinities, with no end. Just of different absolute sizes. Fun stuff to rabbithole down into if you want to melt your brain on a lazy afternoon.
He said I smelled like farts, then I said he did times 10, he replied times a hundred, I pulled out the infinity card, then he replied with times infinity plus one, activating my trap card. I sat him down and for 90 minutes, starting with binary finger counting and Cantor’s diagonalisation argument, I rigorously walked him through infinities and Aleph numbers (only the first 2 in detail, I’m not a monster).
Now he knows the proper retort (not infinity plus one, use Aleph 1). Unfortunately now he’s not sure if numbers are “real” or not because I taught him that natural numbers are the cardinal numbers.
Even more fun: nobody can agree on how many there are (some people say none!), and mathematics is self-consistent regardless of if you assume certain ones definitely doordefinitely don’t exist.
Fun fact: infinities can be different sizes, such that one infinity can be larger than another.
They’re still infinities, with no end. Just of different absolute sizes. Fun stuff to rabbithole down into if you want to melt your brain on a lazy afternoon.
My nephew refuses to talk to me because of this.
He said I smelled like farts, then I said he did times 10, he replied times a hundred, I pulled out the infinity card, then he replied with times infinity plus one, activating my trap card. I sat him down and for 90 minutes, starting with binary finger counting and Cantor’s diagonalisation argument, I rigorously walked him through infinities and Aleph numbers (only the first 2 in detail, I’m not a monster).
Now he knows the proper retort (not infinity plus one, use Aleph 1). Unfortunately now he’s not sure if numbers are “real” or not because I taught him that natural numbers are the cardinal numbers.
Even more fun: nobody can agree on how many there are (some people say none!), and mathematics is self-consistent regardless of if you assume certain ones definitely do or definitely don’t exist.