2,912 reputation
627
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
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 we define the concept of continuity
@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.
Feb
14
comment Game theory question concerning notation
This seems more a terminology question than anything else. In English, a "power of 2" is $2^n$ for some $n$, whereas you'd have to say something more awkward like "the exponent of the largest power of 2" if you wanted to refer to the quantity you had in mind.
Feb
14
comment Why we define the concept of continuity
@IBWiglin I feel like one of the definitions of continuity at a point in terms of neighborhoods of the input and output point is the natural analogue of the $\varepsilon$-$\delta$ definition. And then you can prove that this preimage of open sets business is a nice simple condition equivalent to "continuous at every point".
Feb
12
comment Why are the rational numbers not continuous?
You bring up some important things, but this would be a much better answer if you defined "cut" (and the "sides" thereof) in the text of your answer (if not also "linearly ordered set"). I know what you mean, but I think a reader who is not already familiar with these concepts would not know what you're talking about.
Jan
27
revised Leaving out one of the Peano Axioms
This doesn't really have to do with real analysis.
Jan
27
comment Is 'limit' synonymous with 'radius of convergence'?
let us continue this discussion in chat
Jan
27
comment Is 'limit' synonymous with 'radius of convergence'?
If you wanted to take the corresponding series for the sequence of partial sums of the series whose $n^\text{th}$ term is $a_n$, you'd have to write something like $\sum_{m=0}^\infty\sum_{n=0}^ma_n$. Convergence of $\sum_{n=0}^\infty a_n$ is necessary, but not sufficient for convergence of $\sum_{m=0}^\infty\sum_{n=0}^ma_n$. For example, suppose $\sum_{n=0}^\infty a_n=1$, then $\sum_{m=0}^\infty\sum_{n=0}^ma_n\approx\sum_{m=0}^\infty1=\infty$.
Jan
27
comment Is 'limit' synonymous with 'radius of convergence'?
@OllieFord A sequence can be finite or infinite, but is often infinite. A "series" is just adding up terms of a sequence. If you have $a_n=x*2n$ for every $n$ (starting at $0$), then the infinite sequence is something like $(0,2x,4x,6x,\ldots)$, the corresponding infinite series would be $0+2x+4x+6x+\ldots$, and the "sequence of partial sums" for that infinite series would be $(0,0+2x,0+2x+4x,0+2x+4x+6x,\ldots)$. Does that clear things up?
Jan
27
comment Is 'limit' synonymous with 'radius of convergence'?
@OllieFord, "convergence of a series" is defined to be the same as "convergence of the sequence of partial sums". The phrase "radius of convergence" is related to convergence of a series depending on a parameter. Equivalently, the phrase "radius of convergence" is related to convergence of a sequence of partial sums depending on a parameter".