Chris Eagle
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 Dec 22 awarded Yearling 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 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