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bio website combinatorialgames.wordpress.…
location United States
age 26
visits member for 2 years, 4 months
seen yesterday

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
22
comment Spivak's Axioms of a Number system.
@Berci It was just an example. Neither time nor antimatter is required for the concept of negative numbers, even if you restrict things to real-life implementations. For example, you could handle positive and negative integers with groups of coins, where you may remove any "heads&tails" pair of coins in the same group. But many would say that mathematics isn't necessarily based on any physical setup (in this sense) anyway.
Feb
22
answered Spivak's Axioms of a Number system.
Feb
22
answered Checking differentiability at the origin
Feb
19
comment Decide whether a function has an elementary indefinite integral without determining it!
This may just be a matter of taste, and I know this is how it's written on wikipedia, but I find "an indefinite integral" to be an awkward phrasing. I think of "indefinite integral" as something like "set of all antiderivatives (written in odd ways and sometimes inaccurately)". If you just want one function without a +C or whatever, I figure you want "an (elementary) antiderivative".
Feb
16
comment The equation of parabolas.
As an aside, Desmos seems to handle this more smoothly and it's slightly easier for the user to create their own version for other families of equations.
Feb
16
answered A quick question about a logical negation
Feb
16
asked Name/significance of integral of the square of a probability density function
Feb
16
answered What's the name of the mathematical structure with is an abstraction of things like linear Independence?
Feb
16
comment What is opposite inclusion?
If Martin's answer suited your needs, you can accept it by clicking the checkmark.
Feb
16
comment Integration by parts seems to be infinite, but answer is simple
That fact tells you about indefinite integrals. But you have to remember to plug in the limits of integration to the $uv$ part when you have a definite integral. In other words, $\int_a^bu\mathrm dv=uv\mid_a^b-\int_a^bv\mathrm du$. In particular, your $-y^2\cos(xy)/x$ term should have something like $\mid_{y=-2x-2}^{y=2x+2}$ next to it so you don't forget to plug in. (Separately, a variable outside of an integral with respect to that variable should be a red flag; at best it means you're using a variable in two different ways, but it usually means you've made an error.)
Feb
16
reviewed Approve suggested edit on Continuity of difficult vector function
Feb
16
comment Integration by parts seems to be infinite, but answer is simple
You may have already been aware of this, but be careful when using integration by parts with definite integrals. There shouldn't be a $y$ outside of your $\mathrm dy$ integral on your second line.
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