[FOM] Removing Deep Pathology 1

[W.Taylor at math.canterbury.ac.nz]

> 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


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