welp that was a big sidenote
https://math.stackexchange.com/questions/432293/how-do-you-prove-well-ordering-without-mathematical-induction-and-vice-versa mmmmmmmmmmmmmmmmm ok I see so THAT's why you need well-ordering to define induction
@AskChip i try to be as clear as possible because I'm covering a grad level topic but this book is aimed to last-year undergrads so of course my main source basically explains all of this (some 80+ pages and counting) in 10 pages
@ZevenKorian I always think proofs and exposition should have a clear DAG structure so it can be navigated by skipping bits you don't care about yet, then return to explore the details if you want to see how it works.
@ZevenKorian Now I remember, it was an introduction to a newer version of a math method that was beyond me, even in it's older form. I was so glazed over I can't even remember what the method was for but I think it was a description for an internal procedure for image processing.
@AskChip well, this is singular homology theory which is actually a method you use in image processing so it's not so far away c:
@ZevenKorian So it could be used in image recognition? That's something I was interested in but the math was too involved for me to grasp it except vaguely.
@AskChip homology theory basically designs methods to "scan" the shape of an object using algorithms, which you can then implement as programs (as they are fully automatic)
one example is the Mayer-Vietoris sequence, which is the basic method of computing homology (there are better methods but they may be harder to implement)
@AskChip for example, homology can distinguish between a hollow sphere (like a baloon) and a solid ball of concrete
one example I read about is using homology-assisted AI to detect tumors in an MRI scan
@AskChip a friend of mine actually did her thesis on implementing this method on java, i would joke to her about me doing the mathy details of her thesis
@ZevenKorian Java? OMG that's rich. I kinda liked Java but it scares me to use because it seems so structure resistant, kinda like many older flavors of Basic.
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!