bio  website  dorais.org 

location  Hanover, NH  
age  
visits  member for  4 years, 11 months 
seen  7 hours ago  
stats  profile views  13,275 
I like math and a few other things...
5h

awarded  Generalist 
Oct 15 
awarded  Nice Answer 
Oct 14 
comment 
Is it possible to formulate the axiom of choice as the existence of a survival strategy?
There is also the recent book by Hardin and Taylor  dx.doi.org/10.1007%2F9783319013336 
Oct 14 
comment 
Randall Munroe's Lost Immortals
@StevenGubkin: I think they need to agree on speeds that are linearly independent over $\mathbb{Q}$ to ensure a close encounter. 
Oct 13 
revised 
Face poset of a subcomplex complement
edited title 
Oct 10 
comment 
Forcing is intuitionistic
The settheoretic forcing relation does satisfy doublenegation elimination. (However, the mostly obsolete strong forcing relation does not.) Kripke models also have a relation denoted $\Vdash$ which does not necessarily satisfy doublenegation elimination. Since Kripke models precede forcing historically, I don't think it's Cohen that inspired Kripke. 
Oct 10 
comment 
The periodic architecture underlying the natural numbers
It seems to me your observation is that: every other integer is a multiple of 2, every third integer is a multiple of 3, etc. 
Oct 10 
awarded  Nice Answer 
Oct 7 
comment 
Why do roots of polynomials tend to have absolute value close to 1?
@Joël: While I don't disagree with the craziness, I disagree with the reasoning. While seemingly plausible, Henry's comment is arguably incorrect. While Joseph's answer is enlightening, it does not explain the observed rotational symmetry. There is a lot more to this question than meets the eye... 
Oct 7 
comment 
Why do roots of polynomials tend to have absolute value close to 1?
As seen in my answer, this doesn't seem to explain rotational symmetry at all. In fact, it suggests the opposite. 
Oct 6 
revised 
Why do roots of polynomials tend to have absolute value close to 1?
edited body 
Oct 6 
answered  Why do roots of polynomials tend to have absolute value close to 1? 
Oct 5 
comment 
Why do roots of polynomials tend to have absolute value close to 1?
If we fix the degree at $n$ and the coefficients are iidrvs then the distribution is invariant under $p(z) \mapsto z^np(1/z)$, which means that the distribution of zeros is invariant under $z \mapsto 1/z$. I wonder if there is an equally simple way to see that there has to be some rotational symmetry. 
Oct 4 
revised 
On the definition of the $\alpha$iterable cardinals
fixed (funny!) typo 
Sep 30 
awarded  Explainer 
Sep 28 
comment 
Proofs of the uncountability of the reals.
The issue is that "uncountable" is a negative statement and the natural way to prove a negative is by deriving a contradiction from the positive statement. Note that this is not a proof by contradiction, which consists of proving a positive by deriving a contradiction from the negative... 
Sep 28 
comment 
Proofs of the uncountability of the reals.
The last part relies on the fact that a partition of a set never has more parts than there are elements in the underlying set. This is actually not necessarily true! That is, that fact is a weak form of the Axiom of Choice as explained by Dr. Strangechoice. That said, the argument does work to show that $2^{\mathbb{N}} \gt \aleph_0$ since the contrary assumption $2^{\mathbb{N}} \leq \aleph_0$ entails that $2^{\mathbb{N}}$ is wellorderable. 
Sep 24 
answered  What is the best way to construct an Aronszajn Tree? 
Sep 24 
comment 
What is the best way to construct an Aronszajn Tree?
There is also Stevo's book Walks on ordinals and their characteristics. 
Sep 23 
revised 
Mirror Symmetry for QuaternionicKähler Manifolds
spelling 