28,516 reputation
376165
bio website dorais.org
location Hanover, NH
age
visits member for 4 years, 11 months
seen 7 hours ago

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%2F978-3-319-01333-6
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 set-theoretic forcing relation does satisfy double-negation elimination. (However, the mostly obsolete strong forcing relation does not.) Kripke models also have a relation denoted $\Vdash$ which does not necessarily satisfy double-negation 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 Quaternionic-Kähler Manifolds
spelling