2,727 reputation
625
bio website combinatorialgames.wordpress.…
location United States
age 26
visits member for 2 years, 1 months
seen 2 days ago

I have an amateur interest in combinatorial game theory and rarely update a blog with some basic exposition on the subject (see website).

If you need to contact me, use the e-mail address at this link.


Apr
19
comment Are there 3 trig functions or are there 6 trig functions?
This appears to assume cosine is positive.
Mar
31
answered How to properly determine the limits of a triple integral?
Mar
26
revised Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
deleted 5 characters in body
Mar
26
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
@pbs it was a typo since the text said equal to zero.
Mar
25
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
@sabyasachi yes, but the sequence 3,1,5,1,7,1,... diverges due to oscillation.
Mar
25
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
@sabyasachi I don't think those terms have product limit 1, but Daniel ' s example is fine.
Mar
25
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
The limit of the terms better be 1, but if you're strictly monotonically increasing or decreasing, then all terms are on one side of 1, which means the product won't be 1.
Mar
21
awarded  Nice Answer
Mar
21
comment $\max_{y} \min_{x} f(x,y)$ as motif for exploring mathematics
@alex.jordan for every fixed $ y $, the function of a single variable $ g_y (x)=f (x, y) $ may have a minimum value, but different $ y $ s will give different minima. You can collect them all up into a function of $ y$ called $\min_x f (x, y) $. Since the min of $x^2/2-\pi x $ is $-\pi^2/2$, and similarly if we replace $\pi $ by any arbitrary number $ y $, lilinjn's expression makes sense
Mar
13
answered Terminology: Projection, truncation, elimination
Mar
13
comment Is there a term for parentheses and brackets in equations?
@andre would you be interested in posting that as an answer to remove this from the unanswered list?
Mar
13
revised sum and product of two rational numbers are both integers
fixed the missing x user2357112 referred to
Mar
13
comment Prove that a polynomial has at least one nonreal complex root
For this problem, the technique is to give Descartes' Rule of Signs a better chance, but there is also a generalization of the discriminant method. If your quintic is $x^5+px^3+qx^2+rx+s$ and the discriminant is positive, then it has one real root precisely if at least one of the following is nonpositive: $-p$, $40rp-12p^3-45q^2$, and $12p^4r-4p^3q^2-40p^2qs-88p^2r^2+117pq^2r+125ps^2-27q^4-300qrs+160r^3$. These formulas can be found in demonstrations.wolfram.com/…, which also cites "A Complete Discrimination System for Polynomials".
Mar
13
comment Prove that a polynomial has at least one nonreal complex root
@BohanLu depressing (making a linear substitution to eliminate the term of second-highest order) a polynomial is a key first step in solving polynomials. Depressing a quadratic is basically "completing the square", depressing a cubic/quartic is the first step to solving those equations, and even though quintics don't often have solutions in radicals, depressing them makes them simpler for solving/characterization. (Continued below:
Mar
12
answered mutually exclusive events or not
Mar
12
answered Limit as $x$ approaches 2 is undefined?
Mar
12
comment Simple combinatorics question - caught off guard!
@Darrin I haven't read the book, but this is a direct proof as opposed to a proof by contradiction (or even a proof by induction).
Mar
12
answered Is $…000n$ not a natural number?
Mar
12
answered Prove that a polynomial has at least one nonreal complex root
Mar
12
comment 2nd Question in introductory probability
It would be much easier to point you in the right direction if you posted your thoughts on the problem, where this problem comes from, etc.