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 Apr17 revised A question on Hawaiian earring edited body Apr16 revised A question on Hawaiian earring [Edit removed during grace period] Apr16 comment A question on Hawaiian earring I think the idea of 'reduced form' does not work for $\langle f\rangle$. I think you are viewing $\langle f\rangle$ as $\langle [f_1,f_2]\rangle \langle [f_3,f_4]\rangle\cdots$, but this product does not make sense in a group (infinite product of group elements!) Apr16 comment A question on Hawaiian earring So, you claim that if you have two loops, one passing through origin infinitely often and the another one passing through origin only finitely often can not be homotopic, how do you prove that? Apr16 revised A question on Hawaiian earring edited tags Apr16 asked A question on Hawaiian earring Mar12 comment lim sup of sequence of continuous function from $[0,1]\rightarrow [0,1]$ @LucM: You are right, thanks. Corrected. Mar12 revised lim sup of sequence of continuous function from $[0,1]\rightarrow [0,1]$ edited body Jan1 comment Prove that the real root of $x^3 + x + 1$ is irrational @Beginner: I think it depends on the reviewer/examiner of your proof. If the reviewer is willing to accept the 'Rational Root Theorem' as a standard result (i.e. allow you to use the Theorem) then your proof is fine. Otherwise, you have to provide a proof (not just a link) of the Theorem. Jan1 comment Prove that the real root of $x^3 + x + 1$ is irrational @Beginner: I have added the explanation in the answer. Jan1 revised Prove that the real root of $x^3 + x + 1$ is irrational added 92 characters in body Jan1 comment Prove that the real root of $x^3 + x + 1$ is irrational @Beginner: Note that $p\mid a^3$ and $p\mid ab^2$. Then $p\mid (a^3+ab^2)=-b^3$ and hence $p\mid b$. Jan1 answered Prove that the real root of $x^3 + x + 1$ is irrational Jan1 awarded Autobiographer Dec29 answered Continuous Extension of Maps Sep30 awarded Explainer Jul2 awarded Curious Jul2 awarded Inquisitive Jun15 awarded Yearling Jun14 comment Integer Triangles with Perimeter $n$ @Ozera: I have completed the answer, have a look.