dmonopoly
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 Oct19 awarded Popular Question Sep24 awarded Autobiographer Jul2 awarded Curious Sep16 comment Why compare f(n)/f(n-1) = 1 to solve for the maxima of a discrete function? Hold on... isn't the derivative definition supposed to be $f'(a) = lim_{x \to 0} \frac{f(a+x) - f(a)}{x}$? (Or alternatively $f'(a) = lim_{x \to a} \frac{f(x) - f(a)}{x - a}$)? Sep16 asked Why compare f(n)/f(n-1) = 1 to solve for the maxima of a discrete function? Sep15 comment How to find maxima and minima of a function involving a factorial Intuitively, why does comparing it to 1 help get you the answer? Does it have to do with the Ratio test to see if a series absolutely converges? Apr23 awarded Popular Question Dec16 answered Proving an isomorphism $T_1T_2$ knowing $T_1$ and $T_2$ are 1-1 and onto, respectively Dec16 comment Proving an isomorphism $T_1T_2$ knowing $T_1$ and $T_2$ are 1-1 and onto, respectively Dec16 comment Proving an isomorphism $T_1T_2$ knowing $T_1$ and $T_2$ are 1-1 and onto, respectively I understand how to show $T_1$ is onto and $T_2$ is one-to-one, but afterward, I don't see how I would use that to show $T_1T_2$ is an isomorphism (that's where I get stuck). Dec16 comment Proving an isomorphism $T_1T_2$ knowing $T_1$ and $T_2$ are 1-1 and onto, respectively I see how $T_2(v) = 0$ if the composition = 0, but I don't follow the "then show the composition is [an isomorphism]"... Dec15 comment Proving an isomorphism $T_1T_2$ knowing $T_1$ and $T_2$ are 1-1 and onto, respectively (In case anyone is wondering, this is optional, extra review for a class. The proof is definitely not formal.) Dec15 asked Proving an isomorphism $T_1T_2$ knowing $T_1$ and $T_2$ are 1-1 and onto, respectively Dec15 comment Given a projection T, how do we prove that T(v) = v in this situation? Oh I see now. It's strange how the solution feels.. oddly 'circular' since you start with T(w) = v and then use it again at the end. But thanks! (I guess I'm still getting used to these problems) Dec15 comment Given a projection T, how do we prove that T(v) = v in this situation? Ah, that's a good point - this helps explain where I went wrong. So I need to be careful how I declare my variables and not to conflate the names. Dec15 accepted Given a projection T, how do we prove that T(v) = v in this situation? Dec15 accepted How is $x = 0$ a solution to x' = Ax? Dec15 accepted Midpoint Rule, Trapezoidal Rule, etc.: When the number of intervals increases by a factor of $q$, the approximation error decreases by $r(q) =\;$? Dec15 asked Given a projection T, how do we prove that T(v) = v in this situation? Dec2 answered How is $x = 0$ a solution to x' = Ax?