bio | website | |
---|---|---|
location | ||
age | 28 | |
visits | member for | 3 years, 8 months |
seen | Aug 10 at 13:41 | |
stats | profile views | 593 |
Dec 22 |
awarded | Yearling |
Jun 25 |
awarded | Excavator |
Dec 22 |
awarded | Yearling |
Dec 23 |
awarded | Yearling |
Sep 9 |
comment |
Independence of being an integer
If it's not an integer, then ZFC can certainly prove that, just by approximating it closely enough. |
Jul 15 |
answered | Most 'unintuitive' application of the Axiom of Choice? |
Jun 18 |
comment |
Bijection of proper classes
How does this prove $\kappa^2=\kappa$ for every $\kappa \ge \aleph_0$? It seems to only work for alephs. |
Jun 18 |
comment |
Counterexamples in Algebra?
Every integral domain is a subring of a UFD (for example, its field of fractions). So all you need here is an integral domain which is not a UFD. |
May 31 |
comment |
Ordinal set $\Omega$ : von Neumann definition and modern definition
With what you call the modern definition, the ordinals themselves are not sets (except $0$), so it doesn't even make sense to ask if the class of ordinals is a set. |
May 20 |
comment |
Why the triangle inequality?
Perhaps Michael means that you need the triangle inequality to show that open balls are open, and so the metric topology is generated by the open balls. |
May 17 |
comment |
incompleteness in real analysis
Once you've got quantification over sets, it's easy to define the integers. "$x$ is an integer" means "$x$ is in every subset of $\mathbb{R}$ containing $0$, $1$ and $-1$ and closed under addition". |
May 16 |
comment |
incompleteness in real analysis
The first-order theory of the real ordered field is not categorical in any uncountable cardinal. Such theories are $\omega$-stable, and hence can never define an infinite total order. |
May 11 |
comment |
Mathematical ideas named after places
and the "British Rail metric" |
May 8 |
comment |
Characterization of Tychonoff spaces in terms of open sets
Here's one $\mathbb{R}$-free characterization: a space is Tychonoff iff it has a Hausdorff compactification. Is that the sort of thing you want? |
May 1 |
comment |
How to decompose an infinite set into two isomorphic ones without choice?
@André: Why are you presuming that? The usual definition of "infinite" is "not equinumerous with any natural number". Your property is called "Dedekind infinite". |
Apr 24 |
comment |
Zariski's Main theorem
Crossposted at math.stackexchange.com/questions/34836/zariskis-main-theorem |
Apr 5 |
comment |
solvability of an elementary functional equation
$f(x,0)=g(0)$, not $0$. |
Mar 31 |
awarded | Fanatic |
Mar 25 |
revised |
What are some reasonable-sounding statements that are independent of ZFC?
you can do accents just by using the unicode characters |
Mar 23 |
revised |
Choice function on the countable subsets of the reals
answer expanded question |