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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