Reputation
333,603
Next tag badge:
99/100 score
25/20 answers
Badges
24 298 588
Newest
 Nice Answer
Impact
~5.8m people reached

May
31
comment How to add and subtract functions?
Since for example $(f+g)(x)=f(x)+g(x)$, it is just like solving a system of two ordinary linear equations.
May
31
comment Is there a general algorithm to solve computable integral equation?
I do not know. for several variables I am pretty sure I could routinely push through a reduction to Hilbert's Tenth problem. (One can encode the integers as zeros of solutions of an integral equation.)
May
31
revised Is there a general algorithm to solve computable integral equation?
added 44 characters in body
May
31
answered Is there a general algorithm to solve computable integral equation?
May
31
comment Probability of $\text{Pr}(X+Y=k)$ for two independent random variables $X$ and $Y$
Your first equation is not right, we want $\sum \Pr(X+Y=k|X=l)\Pr(X=l)$. And the conditional probability $\Pr(X+Y=k|X=l)$ is the probability that $Y=k-l$. Now use the distributions of $X$ and $Y$, and a combinatorial identity. To me, it is much easier to view the binomial as a sum of independent Bernoulli.
May
31
comment limit with integral
Hint: Use the mean value theorem for integrals.
May
31
comment What is the pdf of $Z=X/\max(X,Y)$ with $X,Y$ exponentials of lambda parameter?
Nice question for illustrating conditioning. Given the maximum is $X$ (probability $1/2$) then things are easy. Given the maximum is $Y$, note that the conditional distribution of $Y-X$, given $X$, is exponential with parameter $\lambda$.
May
31
answered Why is the expected number coin tosses to get $HTH$ is $10$?
May
31
comment prove that $\text{ord}_k(a)\mid \text{ord}_{k+1}(a)$ where $\text{ord}_k(a)$ is the order of a in $\mathbb{Z}_{p^k}^\ast$
Nothing bad. However, let $m$ and $n$ be any integers such that $m$ divides $n$. Then the order of $a$ modulo $m$ divides the order modulo $n$. Here we are looking at the special case $n=p^{k+1}$, $n=p^k$. But same proof as the one I suggested works in general.
May
31
comment prove that $\text{ord}_k(a)\mid \text{ord}_{k+1}(a)$ where $\text{ord}_k(a)$ is the order of a in $\mathbb{Z}_{p^k}^\ast$
Don't use the Euler function!
May
31
revised prove that $\text{ord}_k(a)\mid \text{ord}_{k+1}(a)$ where $\text{ord}_k(a)$ is the order of a in $\mathbb{Z}_{p^k}^\ast$
added 230 characters in body
May
31
answered prove that $\text{ord}_k(a)\mid \text{ord}_{k+1}(a)$ where $\text{ord}_k(a)$ is the order of a in $\mathbb{Z}_{p^k}^\ast$
May
31
reviewed Leave Open Large Modular Arithematic Exponentiation
May
31
reviewed Leave Open Divergent test for a simple series
May
31
comment What is the length of GH?
From a standard theorem about circles, we have $(CH)(CG)=(12)(12)$.
May
31
reviewed Approve How to calculate the range of $x\sin\frac{1}{x}$?
May
31
comment Proving continuity by epsilon-delta proof for a function of two variables.
With polynomials, there will always be some kind of factorization, because of the theorem that $a$ is a root of $P(t)$ if and only if $t-a$ divides $P(t)$. In several variables, things get more complicated, but still factorization will occur. In our case, it was a simple factorization, because $(x+y)^2$ is a polynomial in the one variable $x+y$.
May
31
answered Proving continuity by epsilon-delta proof for a function of two variables.
May
31
comment Determining the angles of a triangle given the ratio between its edges
You are welcome. Points are not the point of this site. Happy to have helped in the learning.
May
31
comment Determining the angles of a triangle given the ratio between its edges
Well, now that we know $AP$, it is easy. By the equation $x^2+h^2=4$, it is $\sqrt{4-(11/8)^2}$, which simplifies to $\frac{3}{8}\sqrt{15}$. Added: You might be interested in the Heron Formula (Wikipedia) for the area of a triangle with given sides.