May17 awarded Supporter Feb17 awarded Commentator Feb17 comment Question on “Proving $f(x) = 0$ everywhere”Thank you very much Dominic Michaelis! Yes, of course! I stepped away. Feb17 accepted Question on “Proving $f(x) = 0$ everywhere” Feb17 comment Question on “Proving $f(x) = 0$ everywhere”Thank you very much again. You proved $A = B$ by contradiction, which I understand. But what's the intuition for $A = B$? How did you suspect this to be true? Surely, you must've suspected it proving it? Feb17 comment Question on “Proving $f(x) = 0$ everywhere”@Dominic.Michaelis: Great! Thanks. My last follow-up is: $\large{\text{Question 5:}}$ How do we know $f(a - d) = f(a + d$? The function $f(x)$ doesn't have to be symmetric about $x = a$? Feb17 comment Question on “Proving $f(x) = 0$ everywhere”@Dominic.Michaelis: Thank you very much. $\Large{\text{Question 3}}$: Do you mean $A$ is bounded in this question, but $A$ doesn't have to be bounded in general? I'm just a bit confused since you wrote "$A$" is bounded but not necessarily bounded"? $\Large{\text{Question 5}}$: How do we know $A = B$? Feb17 comment Question on “Proving $f(x) = 0$ everywhere”Thank you. Some follow-ups: $\Large{\text{Question 1}}$ : What does “Mh mean”? $\Large{\text{Question 3}}$: Are you using this result: “f is continuous iff if the inverse image of every closed set is a closed set”? Is there something easier? $\Large{\text{Question 4}}$: Isn’t A closed and bounded? $A := {x \in [0,1] : … }$ $\Large{\text{Question 5}}$: Sorry, still don’t see this. How does $$A \leq C \text{ and } B \leq C \text{ and } C = \frac{1}{2}(A + B)$$ imply $A = B = C$? Feb17 comment Question on “Proving $f(x) = 0$ everywhere”Sorry, what did you mean by "did a left another question open?" Thank you for your help so far. Feb17 asked Question on “Proving $f(x) = 0$ everywhere” Jan22 accepted Difference between Kernel for Linear Maps and Group Homomorphisms Jan2 revised Difference between Kernel for Linear Maps and Group HomomorphismsI added an example to show my confusion. I also cut down on repetitive things. Jan2 revised Difference between Kernel for Linear Maps and Group HomomorphismsI added an example to show my confusion. Jan1 asked Difference between Kernel for Linear Maps and Group Homomorphisms Dec30 awarded Editor Dec30 revised S4/V4 isomorphic to S3 - Understanding Attached Tablesedited body; edited title Dec29 asked S4/V4 isomorphic to S3 - Understanding Attached Tables Dec29 comment Quotient Group G/G = {identity}?Thank you. I'll spend some time looking over this. Dec29 awarded Scholar Dec29 accepted Quotient Group G/G = {identity}?