Reputation
687
Next privilege 1,000 Rep.
Create tags
 Mar11 comment What are some difficult integrals done by substitution and elementary functions? I'd like to see the details of how your example is solved. Mar9 asked Over a compact space, the set of continuous functions are everywhere dense in the set of all measurable functions Mar2 awarded Popular Question Feb28 answered Value of the Lebesgue integral of a function Jan1 awarded Yearling Nov28 awarded Nice Answer Nov4 awarded Popular Question Oct25 awarded Popular Question Jul2 awarded Curious Mar6 awarded Self-Learner Feb8 answered Classsifying 1- and 2- dimensional Algebras, up to Isomorphism Jan1 awarded Yearling Oct28 comment The question about the word of “Mathematics”. I think there are actually 8! string which contain the sub-string "math". We count the number of permutation of the 8 objects {e,m,a,t,i,c,s,math}. Oct4 asked Understanding Dini continuity for lifts of circle endomorhpisms May17 accepted Quotient rings of Gaussian integers $\mathbb{Z}[i]/(2)$, $\mathbb{Z}[i]/(3)$, $\mathbb{Z}[i]/(5)$, May17 comment Quotient rings of Gaussian integers $\mathbb{Z}[i]/(2)$, $\mathbb{Z}[i]/(3)$, $\mathbb{Z}[i]/(5)$, That's helpful, thanks. Since R/(2) has just 4 elements, if it were isomorphic to a product of fields, then it would necessarily be isomorphic to Z/(2)xZ/(2). But $i^2=1$ in R/(2), and every element of Z/(2)xZ/(2) when squared equals itself. So... From the unusual phrasing of the question, I suppose R/(5) is isomorphic to a product of fields. Is this right? Would that product be Z/(5)/Z/(5)? May17 asked Quotient rings of Gaussian integers $\mathbb{Z}[i]/(2)$, $\mathbb{Z}[i]/(3)$, $\mathbb{Z}[i]/(5)$, May16 awarded Caucus Jan1 awarded Yearling Sep3 accepted $f,g$ continuous functions, $f$ strictly increasing, non-vanishing: $\int_a^bg(x)(f(x))^n\,dx=0$ for all $n$ $\Rightarrow g\equiv 0$