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Sep
1
answered Change of variable using dirac delta function
Sep
1
comment Proving $[(P\lor Q)\land(P\to R)\land(Q\to R)]\to R$ is a tautology without using a truth table?
what inference rules do you have? surely implication elimination, i.e. $(a\rightarrow b)\land a\implies b$
Sep
1
comment Find $\sum\limits_{n=1}^{\infty}\frac{n^4}{4^n}$
Fourier series instead of generating functions -- nice
Sep
1
comment Understanding Little Oh Notation Proof - Prove the function$ f(n) = 12n^2 + 6n\ \ is\ \ o(n^3)$
if for any $c$ we can find $n_0$ such that $0\le f(n)\le cg(n)$ holds for $n\ge n_0$ then it follows that $n\ge n_0$ is sufficient to give a strict bound $0\le f(n)<dg(n)$ for $d>c$. So if we want to show for $d$ that there is $n_0$ so that $0\le f(n)< dg(n)$ for $n\ge n_0$, just pick a $c$ such that $0<c<d$ (e.g. $c=d/2$) and $n_0=\frac{18}c=\frac{36}d$ will work for the strict inequality in $d$.
Sep
1
answered Find $\sum\limits_{n=1}^{\infty}\frac{n^4}{4^n}$
Sep
1
answered Understanding Little Oh Notation Proof - Prove the function$ f(n) = 12n^2 + 6n\ \ is\ \ o(n^3)$
Aug
30
comment Showing for any real number $\lfloor a\rfloor+1>a$
how are you defining $\lfloor a\rfloor$? once you specifically have that it should be obvious
Aug
30
comment Generalizing limits of sums, products, and quotients of sequences to abstract topological spaces?
@EthanAlvaree en.wikipedia.org/wiki/Algebra_over_a_field
Aug
22
comment Polynomial equations of degree larger than 4
finding cube roots is trivial by de Moivre's theorem: $z^3=re^{it}$ gives $z\in\{\sqrt[3]{r}e^{it/3},\sqrt[3]{r}e^{i(t+2\pi)/3},\sqrt[3]{r}e^{i(t+4\pi)/3}‌​\}$
Jul
31
comment Asymptotic direction
just an fyi: the second derivative doesn't live in the tangent space or bundle
Jul
31
comment Proof that the Runge Phenomenon occurs
the reason is given right here
Jul
31
comment Dedekind Construction Of Real Numbers
"in this topology" -- you mean the product topology on $\mathbb R^2$?
Jul
31
revised Trying to understand why 2 times the sum of consecutive integers from 0 to n is equal to n times n+1
edited body
Jul
31
answered Trying to understand why 2 times the sum of consecutive integers from 0 to n is equal to n times n+1
Jul
31
answered Quadratic equation with several variables
Jul
31
comment Reciprocals of theta functions
Weierstrass elliptic functions have second-order poles on a lattice generated by $\omega_1,\omega_2$
Jul
31
answered incremental computation of standard deviation
Jul
31
comment why does the reduced row echelon form have the same null space as the original matrix?
@beginner left multiplication of elementary matrices does not preserve the column space; right multiplication, however, does -- though then this does not preserve the null space.
Jul
31
answered Basis of a product vector space
Jul
31
answered why does the reduced row echelon form have the same null space as the original matrix?