3,100 reputation
1427
bio website dorais.org
location Hanover, NH
age
visits member for 4 years, 5 months
seen yesterday

I like math and a few other things...


May
7
asked A natural example in category theory
May
7
awarded  Caucus
Apr
26
comment What is Baire's zero-dimensional metric space?
Additional context would help, but it's usually this one - en.wikipedia.org/wiki/Baire_space_(set_theory)
Apr
26
awarded  Informed
Apr
5
comment Uniform distribution with probability density function. Find the value of $k$.
How many types of mathematicians are there?
Mar
27
awarded  Good Answer
Jan
7
comment What are the differences between rings, groups, and fields?
That used to be the case but most authors today define a ring to have $1$. The unusual looking term rng is sometimes used for the concept without $1$.
Dec
27
comment Is empty set a proper subset of itself?
$B \setminus A \neq \varnothing$ does not imply that $A$ is a subset of $B$. (But, if it is, then it is indeed a proper subset.)
Dec
5
answered Questions about generalizations of the Principle of Dependent Choices
Dec
4
answered Proofs whose length depends on the input
Sep
18
answered Does every nonempty definable finite set have a definable member?
Aug
19
answered Borel linear order cannot have uncountable increasing chain
Aug
19
comment Borel linear order cannot have uncountable increasing chain
I had missed the link! The author cites Harrington and Shelah, who did prove the result I recalled earlier. I guess it would be best to check that reference. @William: No. There are no uncountable wellordered Borel chains at all so that weaker variant is vacuously true.
Aug
19
comment Borel linear order cannot have uncountable increasing chain
This is true if chain is replaced by wellordered chain. In other words, a Borel linear order cannot contain a copy of $\omega_1$ or its reverse. I would guess that's what is meant, otherwise "increasing or decreasing" is not very meaningful. Where is this from?
Aug
16
comment What is actually “relatively consistent”?
"If a system is not complete, then it is consistent." Seeing that complete usually means "proves $\sigma$ or $\lnot\sigma$ for every sentence $\sigma$" and that consistent usually means "does not prove every sentence $\sigma$," a system that is not complete must be consistent. There are variations but, in any case, I don't think your second sentence exactly says what you meant to say.
Aug
14
awarded  Quorum
Aug
6
comment Axiom of choice - to use or not to use
Also, the axiom of choice is not necessarily non-constructive. For example, full choice is valid in constructive type theory.
Aug
3
awarded  Revival
Aug
3
comment Proving that the set of algebraic numbers is countable without AC
And yes, countable means $\leq \aleph_0$ and, in particular, infinite Dedekind finite sets are "uncountable" in ZF. So one shouldn't think that "uncountable" means "large" in ZF...
Aug
3
comment Proving that the set of algebraic numbers is countable without AC
Yes, your answer is perfectly correct, my comment was just an addendum. Since I had a chance to look it up, the reference is: Hodges, Läuchli's algebraic closure of $\mathbb{Q}$, Math. Proc. Cambridge Philos. Soc. 79 (1976), 289-297. ams.org/mathscinet-getitem?mr=422022