[FOM] Removing Deep Pathology 1

[Hendrik Boom]

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