Eric Thoma
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 1d comment Characterization of measurable sets $E$ with $|E|_e<\infty$ Late to the party but: $\lvert E{\rvert}_e < \infty$ is needed for the other direction to show that when writing an open set $G \supset E$, $\lvert G-E\rvert < \epsilon$ as a countable union of nonoverlapping intervals, the tail of the union has small measure. This direction does not appear to need this, since the finite union of intervals is so nice and the other $N_1$ and $N_2$ are already small. Mar7 comment How could I prove whether the infinite series $n!/n^n$ converges or diverges? @JulianRachman "By this result, we can see that the series does not diverge, however it is still inconclusive that the series converges." This is not right at all. The theorem you used gives sufficient conditions for convergence, not necessary. And "converges xor diverges" is a tautology, so the statement itself does not make sense. (edit: it's fixed now, though only the ratio test is necessary, undid -1). Feb22 answered this is not a vector space,is it? Dec21 awarded Caucus Sep30 awarded Explainer Sep24 awarded Autobiographer Jul12 awarded Yearling Apr9 comment Prove that if b is coprime to 6 then $b^2 \equiv 1$ (mod 24) Since $b^2$ is a perfect square, we have that $b^2 = 1,4,9,16$ modulo $24$. All of these, besides $1$, require that $2 | b$ or $3 | b$. Mar9 comment Is this fraction even possible to put into partial fractions? @Wolff Think inverse trigonometric functions. Feb6 comment Real Analysis Question concerning existence of curve and derivative? Suppose $f(0) \ne 0$. Use continuity of $f$ to obtain a contradiction. Jan31 comment % of my equivalent human life hunting a fly for 5 minutes before I kill it, if its lived for 3 days and myself for 40 years House flies usually live for 15 to 30 days once hatched from pupal stage, though you may very well have been chasing a 3-day-old fly. Jan31 answered How to find the inverse function? Jan24 comment Does an element of a group to the 0th power equal the identity? In other words, the assignment of $x^0 = 1$ plays nice with $x^ax^b = x^{ab}$ for all $a$ and $b$, a desirable property. Jan19 comment Does this equation have positive integer solutions? In other words, combining any two Pythagorean triples gives a solution. Jan5 comment How do I show using math symbols “get quotient without remainder” Try $\lfloor 10/3 \rfloor=3$. This is the "floor" operation and gets rid of any decimal. Jan2 comment How find this integral Your bounds are for $t$, but you treated them as if they were for $\theta$. Notice that $\theta = \sin^{-1} t$, so you can easily switch back. Dec31 answered How many even numbers are there in a set $\{x_1, x_2 … x_n\}$ Dec30 answered The number of ways in which 6 pencils can be distributed between two boys such that each boy gets at least one pencil is Dec29 revised Project Euler - 34 / Find a mathematical approach for upper bound deleted 8 characters in body Dec29 revised Project Euler - 34 / Find a mathematical approach for upper bound added 294 characters in body