3,088 reputation
728
bio website combinatorialgames.wordpress.…
location United States
age 27
visits member for 2 years, 6 months
seen 1 hour 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.


Feb
16
answered Factorization of a degree three polynomial
Feb
16
comment A game of Chess - Ideal Solution
@DanielRust Whether "group theory" is used is arguable, but Elkies identifies boards/chunks of boards with elements of the abelian group of short Games, and adds them (see, for example, the sole occurrence of the word "total" in the paper). I mentioned the inverse just as a response to "[groups are] not applicable because moves aren't invertible".
Feb
16
comment A game of Chess - Ideal Solution
@Daniel Not to all of chess, but certain contrived endgames/chess puzzles have solutions based on combinatorial game theory, which involves groups (see Noam Elkies' paper). In this context, the inverse of a game position (or a component of one) is the same position with Black and White switched.
Feb
15
comment Why are the surreals considered “recreational” mathematics?
I agree with most of what you said, but I think most of the structure/theorems about the surreals are not even necessary for CGT. Does, say, the multiplicative structure of the surreals have any bearing on Games?
Feb
15
comment Mathematical Notation and its importance
possibly related: math.stackexchange.com/questions/555895 and math.stackexchange.com/questions/93922 and mathoverflow.net/questions/42929
Feb
15
revised Mathematical Notation and its importance
edited tags
Feb
15
comment Is it possible to have numbers that are to Hyperreal numbers what Hyperreals are to Reals numbers?
@joeA I think I fixed the tags.
Feb
15
revised Is it possible to have numbers that are to Hyperreal numbers what Hyperreals are to Reals numbers?
tags
Feb
15
reviewed Reject suggested edit on Algebra 2 Bonus Question
Feb
15
revised A question about indeterminate forms
retagged
Feb
15
comment Showing something is not onto?
I think I just forgot what the original question was, so never mind that part.
Feb
15
answered A question about indeterminate forms
Feb
15
comment Showing something is not onto?
Did you mean "saying that $T$ is not surjective"? In any case, the last sentence is the key argument and there's no need to argue by contradiction. (I was not the downvote, but your second sentence is false as stated.)
Feb
15
comment Every truth function of the inderterminates X and Y is an iterated composition of negations and disjunctions.
I think the "every truth function" bit means all 16 functions that take two truth values and return one. It would have been more fun if user123943 were asked to prove that "NOR" suffices all on its own.
Feb
15
comment What exactly do the sin, cos, tan buttons do on a calculator?
This page claims that (simpler?) calculators don't actually use the Maclaurin series. Do you know which ones do/don't?
Feb
15
answered Showing something is not onto?
Feb
15
answered Curiosity with surreal numbers
Feb
15
comment Why are the surreals considered “recreational” mathematics?
If you don't want infinite numbers, take numbers bounded by finite integers (or bounded by "something with finite ordinal birthday"). If you want to define the reals, they're "the finite surreals $r$ simplest less than all $r+q$ and greater than all $r-q$ for positive rationals $q$" (You could replace rationals with dyadic rationals, the surreals with finite birthdays, if you prefer.) It is absolutely not the case that a new set theory is required to define the surreals (there is no logical problem). However, the definition might be a little nicer-looking in such a "two-sided set theory".
Feb
15
answered Why are the surreals considered “recreational” mathematics?
Feb
14
comment Why did we define the concept of continuity originally, and why it is defined the way it is?
@IBWiglin Let me be precise: I feel like definitions similar to "$f$ is said to be 'continuous at $p$' if for every neighborhood $N$ of $f(p)$ there is a neighborhood $M$ of $p$ such that the image of $M$ is a subset of $N$." (which makes sense for any pair of topological spaces) are the natural analogue of the $\varepsilon$-$\delta$ definition for metric spaces. Then separately, you can prove that the function is continuous at every point if and only if the preimage of every open set is open.