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Let $A = \begin{pmatrix} \cos \delta & -\sin \delta & 0 \\ \sin \delta & \cos \delta & 0 \\ 0 & 0 & 1 \end{pmatrix}$, and let $B = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos \delta & -\sin \delta \\ 0 & \s …

Since it is regular of countably infinite degree, it is isomorphic to the union of Bruhat-Tits trees for PGL2(F) as F ranges over unramified extensions of a local field. The automorphism group theref …

This is just a minor amplification of one of Terry Tao's points. For any prime $p$, the ring $\mathbb{Z}_p$ of $p$-adic integers forms an open compact additive subgroup of $\mathbb{Q}_p$, the complet …

This is not a complete answer, but it might help with some higher-rank computations if you decide to do them. Out of some possibly irrational exuberance, I guessed that if there are any solutions, th …

While you might conceivably get convergence a.s., you won't get convergence always, since one could have a sequence where only the vertex not adjacent to the longest edge is replaced. This would forc …

For question 1, one example of interest comes from the energy eigenfunctions of the one dimensional quantum harmonic oscillator. The Hilbert space is separable, and the Hamiltonian satisfies your con …

My experience with foundations is rather scant, but I've run into some types of objects that seem to resist the sort of set-theoretic encoding schemes via Kurowski tuples that are rather common for ob …

I think one's standards of intuitiveness depend strongly on one's background. Even if a picture seems unintuitive at first, it can be helpful later. If you're an algebraist, I'd suggest the multipl …