0: I did most of the topological fixed point exercises on the 20th & the morning of the 21st, and then did most of the iteration fixed point exercises on the 21st. I liked the diagonalization ones the best, then the topological ones come in second (unsure how to explain why—just feels like coolness : complexity is lower), and the iteration ones come last (I think because I already know the contraction mapping principle very well, and unlike the topological ones there isn’t a cooler proof to dazzle me with; the lattice ones didn’t feel that novel given the spiritual similarity).
1: As a subpoint, the fact that there’s a unique closest point in a closed convex set S to any point p in euclidean space was pretty neat, and further acts as an enticing advertisement for me to read Boyd’s Convex Optimization
2: Apparently, the Wikipedia page on fixed point theorems really does basically just list variations on Diagonalization/Brouwer/Iteration. Perhaps I should take the couple best, and write a post on them?
April 20-21
0: I did most of the topological fixed point exercises on the 20th & the morning of the 21st, and then did most of the iteration fixed point exercises on the 21st. I liked the diagonalization ones the best, then the topological ones come in second (unsure how to explain why—just feels like coolness : complexity is lower), and the iteration ones come last (I think because I already know the contraction mapping principle very well, and unlike the topological ones there isn’t a cooler proof to dazzle me with; the lattice ones didn’t feel that novel given the spiritual similarity).
1: As a subpoint, the fact that there’s a unique closest point in a closed convex set S to any point p in euclidean space was pretty neat, and further acts as an enticing advertisement for me to read Boyd’s Convex Optimization
2: Apparently, the Wikipedia page on fixed point theorems really does basically just list variations on Diagonalization/Brouwer/Iteration. Perhaps I should take the couple best, and write a post on them?