Austin Mohr
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 9h comment Methods for solving for partial fraction coefficients. I present both. The first shows what's really going on - two polynomials are identical provided their coefficients agree. The second shows a nice "trick" that generalizes elsewhere - if a statement is true for every $x$, then it's true for any particular $x$. Feb 3 comment If you roll a die two times, what is the probability the sum of the upturned faces equals $7$? @ClementC. The outcomes $(1,6)$ and $(1,1)$ are equally likely, but the outcomes $\{1, 6\}$ and $\{1,1\}$ are not, since $\{1,6\}$ corresponds to both $(1,6)$ and $(6,1)$. Jan 30 comment Number of $2 \times 2$ images in RGB This is correct provided you don't take any weird symmetry considerations into account. Jan 28 comment Are there sets in the K-Topology that aren't open in the standard topology? NWU Topology thanks you. :) Jan 28 comment Limit point Compactness does not imply compactness counter-example A space is countably compact provided every countable open cover admits a finite subcover. This is strictly weaker than compactness, which requires that every open cover admits a finite subcover. Jan 28 revised Partial Fractions Integration Help edited title Jan 26 comment Closed sets and how they relate to open balls? Some familiar examples on the real line: $(0,1)$ is open, $[0,1]$ is closed, $[0,1)$ is neither open nor closed, and $\mathbb{R}$ is both open and closed. Jan 25 comment Total Number of Equivalence classes of R One might also want to demonstrate that every possible truth table is realizable by some proposition. That is, given a truth table $T$, show there is a proposition whose truth table is $T$. Jan 24 comment Link to question regarding treating differential operator as a ratio Is it one of these answers? math.stackexchange.com/questions/21199/… Jan 24 comment What is the largest value of $n$ where $\lg(n) \le 1,000,000$ The symbol $\operatorname{lg}$ typically refers to the logarithm with base 2. Jan 23 revised How Many Ways to Make a Pair Given Five Poker Cards edited title Jan 21 comment $4$-regular graph with exactly one perfect matching I've all but convinced myself that you cannot obtain the desired graph by adding edges to the 3-regular graph I linked to. You're always forced to put an edge between vertex "clusters", and that seems to break the example. Jan 21 comment $4$-regular graph with exactly one perfect matching If a 4-regular graph has exactly one perfect matching, then removing the edges of that matching should leave a 3-regular with no perfect matching. Probably you can carefully add edges to this graph in such a way that you create exactly one perfect matching. Jan 20 comment Why can't you have more turning points than the degree? @BernardMasse I was thinking along the same lines, but in general I think you may have to allow for $cp(x) = a$ for some small constant $c$. This would pull the turning points close together so that they cross the same horizontal line. Jan 19 comment Why can't you have more turning points than the degree? A polynomial may have more turning points than real zeroes (unless you take "zero" to mean "real root" already). Jan 19 comment Why can't you have more turning points than the degree? The question is marked algebra-precalculus. Does that mean you do not want answers that involve calculus? Jan 12 revised Determine all positive rational numbers $r \neq 1$ such that $r^{\frac{1}{r-1}}$ is rational? edited body Dec 26 comment A finite set has no limit points Are you speaking of general topological spaces or of the real line in particular? Dec 23 comment An interesting Sum involving Binomial Coefficients I hope the community will allow me a frivolous comment: I always appreciate seeing your complex analytic contributions to these identity questions. Dec 8 revised Do All Hamiltonian Paths in a Graph with Several Disjoint Ham-Paths Have the Same Number of Edges? edited title