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visits member for 3 years, 10 months
seen Aug 10 at 13:41

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