3,123 reputation
729
bio website combinatorialgames.wordpress.…
location United States
age 27
visits member for 2 years, 7 months
seen 8 hours 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.


May
26
answered What is the opposite of a robust system?
May
26
comment How exactly is $i=\sqrt{-1}$ related to $\mathbb{C}$ being a closed algebraic field?
It's important to note (and the links clarify this) that the Quaternions are not what you get when you have the same goal (algebraic closure) but happen to be working with matrices, but rather something reminiscent of the complex numbers you can get when you change/weaken the goal.
May
26
comment How exactly is $i=\sqrt{-1}$ related to $\mathbb{C}$ being a closed algebraic field?
@Nikos $\sqrt\pi$ is the number that you square to get $\pi$. Every positive number has a positive square root: If you believe it for rationals, just take the limit of a sequence of rational numbers whose square is not quite big enough, but whose squares tend to the number in question.
May
26
answered How exactly is $i=\sqrt{-1}$ related to $\mathbb{C}$ being a closed algebraic field?
May
26
answered Are there combinatorial games of finite order different from $1$ or $2$?
May
26
comment Are there non-zero combinatorial games of odd order?
The proof of "no (nonzero) games of odd order" is too long to fairly reproduce here. I suppose it's worth mentioning that the key result (which is not so easy to prove) is that if $G$ has finite order and birthday $n$, then $2^nG=0$.
May
25
answered Interesting sequence question
May
22
awarded  Revival
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