This is an interesting article describing Cantor's original proof that the real numbers cannot be enumerated, which has the somewhat-shocking implication that some infinities are bigger than others!
This is an interesting article describing Cantor's original proof that the real numbers cannot be enumerated, which has the somewhat-shocking implication that some infinities are bigger than others!
Georg Cantor and his influence was my favourite part of my favourite class in university, which included a history of mathematics, a whole lot of set theory, and was my introduction to Proofs from...
Georg Cantor and his influence was my favourite part of my favourite class in university, which included a history of mathematics, a whole lot of set theory, and was my introduction to Proofs from THE BOOK which every aspiring mathematician (or math enthusiast) should read. I should note it's been years and I don't actually recall if this is one of the Proofs from THE BOOK, but it does have the stark beauty and intuitive graspableness that those proofs have.
Quite interesting. This proof has a much more standard flavor of analysis involving upper/lower bounds, lim inf/sup sort of things, but it's not as memorable or transparent as the canonical...
Quite interesting. This proof has a much more standard flavor of analysis involving upper/lower bounds, lim inf/sup sort of things, but it's not as memorable or transparent as the canonical diagonal proof.
FYI, the Wiki article on this proof is pretty good.
This is an interesting article describing Cantor's original proof that the real numbers cannot be enumerated, which has the somewhat-shocking implication that some infinities are bigger than others!
This is giving me flashbacks to my CS Discrete Mathematics class where we had to prove this theorem on exams...
Yeah same. I wish I was as interested in it then as I am now.
Georg Cantor and his influence was my favourite part of my favourite class in university, which included a history of mathematics, a whole lot of set theory, and was my introduction to Proofs from THE BOOK which every aspiring mathematician (or math enthusiast) should read. I should note it's been years and I don't actually recall if this is one of the Proofs from THE BOOK, but it does have the stark beauty and intuitive graspableness that those proofs have.
Quite interesting. This proof has a much more standard flavor of analysis involving upper/lower bounds, lim inf/sup sort of things, but it's not as memorable or transparent as the canonical diagonal proof.
FYI, the Wiki article on this proof is pretty good.