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# 36 Actions

 Dec 15 awarded Caucus Oct 10 awarded Autobiographer Apr 23 comment Becoming Better at Math Embrace failure. It is part of life. Don't give up. Apr 14 comment Limit is found using polar coordinates but it is not supposed to exist. @heropup: Can I ask how you made this plot? Jan 15 awarded Yearling Nov 21 comment Find All Cycles (Faces) In a Graph @hardmath Thank you very much for this algorithm description, it has helped me wrap my head around how I can enumerate the cycles in a planar graph. Jun 13 comment Intuitive meaning of Exact Sequence What is a "syzygy" because I sure don't know: ams.org/notices/200604/what-is.pdf May 14 awarded Caucus Mar 1 comment Uncertainty of process used in simple proof that there exists no rational number whose square is 2. @AlexHeuman: What I was trying to say: why does the theorem statement mention $\sqrt{2}$ when clearly you are trying to prove something general. That is something akin to stating a corollary of a theorem, proving a general theorem, then applying the theorem to show the corollary, without ever stating the general theorem you wanted to prove. Its just bad math writing style in my opinion. Mar 1 comment Uncertainty of process used in simple proof that there exists no rational number whose square is 2. How can this be the proof when you make no mention of $\sqrt{2}$? Feb 19 answered What is the problem in happily using the MacLaurin expansion of $e^x$ with $e^{ix}$? Jul 4 answered Free probability background requirements Mar 13 comment I have to show that the matrix $M^TM$ is SPD if and only if the columns of the matrix M are linearly independent Since M is m x n I think eigenvalue analysis is not general enough. It only deals with linear operators from one linear space mapping to the same linear space. Mar 2 comment Showing a function is holomorphic Usually commuting limits and integrals is allowed when uniform convergence is satisfied. That is, if you a (2 dimensional) series of functions $f_{n,m}(x)$ then if $f_{n,m}$ converges uniformly we have $\lim_{n\rightarrow \infty}\lim_{m\rightarrow\infty}f_{n,m}(x)=\lim_{m \rightarrow \infty}\lim_{n \rightarrow \infty}f_{n,m}(x)$, but without uniform convergence, this result is not true in general. Feb 5 awarded Commentator Feb 5 comment Solving a Recurrence Relation/Equation, is there more than 1 way to solve this? You can show your appreciation by upvoting ... +1 Feb 5 awarded Student Feb 5 comment is this line of thinking valid for quick solving? I think the OP reasoning is a great way to use intuition to guess the answer, then prove it. But I feel you did correctly show that using that intuition, you can also write the same thing as a limit of $\infty \cdot 0$ which should always raise red flags. Also, to be nit picky, part of the reason the intuition doesn't work here is because $\lim (a+b) = \lim a + \lim b$ if and only if $\lim a$ and $\lim b$ exist and are finite. Feb 5 awarded Scholar Feb 5 accepted Minesweeper Deterministic Solvability Conditions