@ZevenKorian Trick question are just mean. I include vague and marginal questions in that junkheap.

@ZevenKorian Hmm, I could swear I've seen that sidenote somewhere, but in English.

@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

ℍᵃⁿⁿᵃʰ 🍀@ZevenKorian@mathstodon.xyzit basically says that to prove a property Q(n,m) via "double induction" you first prove P(n)=Q(n,1) by induction (solid arrows) and then prove R(m)=Q(n,m) by induction (dashed arrows)