[FOM] Removing Deep Pathology 1
Hendrik Boom
hendrik at topoi.pooq.com
Tue Aug 18 14:47:34 EDT 2015
Let me vote on these, to the extent that a voting is even relevant here.
On Tue, Aug 18, 2015 at 06:05:45PM +1200, W.Taylor at math.canterbury.ac.nz wrote:
> >There is an aspect of mathematics that I call
> >
> >*deeply pathological*
>
> I like the f(x+y) = f(x) + f(y) example, as a case of deep pathology.
>
> May I ask the list, for clarification, where the following might come
> on the spectrum from "superficial pathology" to "deep pathology".
>
> 1) The Cantor subset of [0,1]
No.
> 2) Peano's space-filling curve.
No.
> 3) The existence of a non-measurable subset of [0,1]
> 3a) " " " " non-Borel " " "
Yes.
>
> 4) The partition of 3-space by (infinitely long) non-parallel lines.
> 4a) " " " " " non-parallel circles.
If it's the one I vaguely remember, no. But it's truly beautiful.
> 5) The partition of [0,1]^2 by countably many graphs and co-graphs.
abstain. Not familiar enough.
> 6) The existence of a non-computable function (from N to N).
If you're talking about partial functions, no. If you're talking about
total functions, yes.
>
> 7) The existence of a non-definable (countable) ordinal.
yes.
> 8) The existence of an uncountable ordinal.
Yes.
-- hendrik
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