[FOM] Removing Deep Pathology 1
W.Taylor at math.canterbury.ac.nz
W.Taylor at math.canterbury.ac.nz
Tue Aug 18 02:05:45 EDT 2015
> 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]
2) Peano's space-filling curve.
3) The existence of a non-measurable subset of [0,1]
3a) " " " " non-Borel " " "
4) The partition of 3-space by (infinitely long) non-parallel lines.
4a) " " " " " non-parallel circles.
5) The partition of [0,1]^2 by countably many graphs and co-graphs.
6) The existence of a non-computable function (from N to N).
7) The existence of a non-definable (countable) ordinal.
8) The existence of an uncountable ordinal.
Thanks in advance for all clarifications.
Bill Taylor
----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.
More information about the FOM
mailing list