8,681 reputation
21838
bio website gottwurfelt.wordpress.com
location San Francisco, CA
age 30
visits member for 4 years, 1 month
seen 18 hours ago

Quantitative analyst and math blogger.


Sep
7
awarded  Civic Duty
Sep
6
comment $5^n+n$ is never prime?
In fact, if $\sum 1/log f(n)$ diverges and there's no covering set there should be infinitely many primes of form $f(n)$.
Sep
5
comment How to calculate the number of decimal digits for a binary number?
Just to confirm this for you: log(2)/log(10) is irrational. The proof is simple: clearly log(2)/log(10) is positive. So assume it's a positive rational number, i. e. that log(2)/log(10) = p/q where p and q are nonzero positive integers. Then you have p log 10 = q log 2. Exponentiating both sizes, 10^p = 2^q. But 10^p is divisible by 5 and 2^q isn't.
Sep
5
comment Finding a clever solution to a game of chance
This is a good method, but $\lim_{n \to \infty} q_n = 0$, right?
Sep
4
comment Finding a function that approaches another function
This is a nice solution! To anyone checking this, you should know there's one small error: after the third differentiation, you need to multiply by x one more time.
Aug
30
awarded  Student
Aug
30
asked What do all the $k$-cycles in $S_n$ generate?
Aug
27
comment Finding the units' digit of large quotients
This reminds me of the following problem of Richard Stanley: "Find a positive integer $n<10,000,000$ such that the first four digits (in the decimal expansion) of $n^{1,000,000}$ are all different. The problem should be solved in your head." The answer is at math.mit.edu/~rstan/milsol.html .
Aug
23
answered Why is the 3D case so rich?
Aug
22
comment very simple conditional probability question
Thanks! Thanks again, because comments have to be fifteen characters or more!
Aug
22
answered very simple conditional probability question
Aug
21
comment Can this standard calculus result be explained “intuitively”
Just a thought: it's probably easier to find an intuitive explanation of the equivalent d/dx arctan x = 1/(1+x^2).
Aug
19
comment Companions to Rudin?
I'm not familiar with these. But I found Bergman's companion to Lang's Algebra quite useful when I was studying from that book, so consider that a qualified recommendation for Bergman's course materials in general.
Aug
19
comment What is the expected number of runs of same color in a standard deck of cards?
More generally, a deck with $2k$ cards, $k$ of each color, has expected number of runs $k+1$.
Aug
18
comment What is the importance of the Collatz conjecture?
$500 is a fairly large prize by Erdos' standards. See math.ucsd.edu/~fan/ep.pdf and math.niu.edu/~rusin/known-math/93_back/prizes.erd . (These are the only two lists I could find with dollar figures on them; neither actually includes the Collatz problem.)
Aug
18
comment Averaging 2 roots of a cubic polynomial
Just out of curiosity, which generalizations have you tried? For example, are you averaging two roots of the higher-degree polynomial, or all the roots except one?
Aug
15
comment Is there a name for $[0,1]$?
"Numbers in the unit interval" works.
Aug
14
awarded  Commentator
Aug
14
comment Fundamental group of the double torus
However, if the original answer had included the magic words "see Exercise 0.2", this would be a perfectly fine answer. (Note for those who don't follow the link: Baez gives the solution there. I don't think it makes sense to just give a link to where somebody has asked a question.)
Aug
14
comment Asimov quote about “eight million trillion” arrangements of amino acids
Asimov was trained as a chemist. I think he would have known better and someone else made a mistake.