2 ms·
Asking ChatGPT about cases from “Counterexamples in Analysis”
- perihelions 4y agoMore comments/discussion on Mastodon, https://mathstodon.xyz/@johncarlosbaez/110035669587643133 https://mathstodon.xyz/@johncarlosbaez/110035669587643133
- karpierz 4y agoIn case someone wants an example of a function which is continuous nowhere, but whose absolute value is continuous everywhere: f(x) = 1 if x is rational f(x) = -1 if x is not rational Edit: in all this excitement, I should've just read to the end of the article Edit: for the second question, take the function: f(x) = 0 if: the binary representation of it contains infinite 1s f(x) = total # 1s in the binary representation of x if: the binary representation has a finite number of 1s