who says that students don't have manners?

in my proofs class today, one of my students walked up to me and asked if a friend

.. who was visiting the university?
i forgot to ask ..

could sit in on the lecture today. several things came to mind, right away.

1. my students don't realise that (A) i can't remember who attends lectures and who doesn't, as well as (B) i've never enforced a mandatory attendance policy.
   
   heck: if you can learn the material, by reading the book and doing examples on your own, then you're doing quite well!


2. when i was a student, i don't think i would have bothered asking permission. actually, i probably wouldn't have attended class.
   
   instead, if my friend came to visit then i'd probably take them on a tour of the city.

it was quite considerate of the student to ask, though, so i said yes. let's hope that the visiting friend wasn't bored out of his mind ..!

---

as for what i discussed, today was cantοr's intersectiοn theorem. after discussing an alternate version (for when the conclusion gives a unique limit point) i pointed out that one can actually develop from this number systems of different bases ..

not only decimal, but binary .. and just to mess with their heads, base $\sqrt{2}$.
for example,
$$(10101)_{\sqrt{2}} = 1(\sqrt{2})^4 + 1(\sqrt{2})^2 + 1(\sqrt{2})^0 = 4+2+1 = 7$$
and
$$\frac{9}{5} = (1.00100000001\ldots)_{\sqrt{2}}$$
so sue me: i get bored easily. q-: