The following excerpts
from Coxeter's
Projective
Geometry
sketch his attitude toward geometry in characteristic two.
"... we develop a self-contained account... made
more 'modern' by allowing the field to be general
(though not of characteristic 2) instead of real or complex."
The "modern" in quotation marks may have been an oblique
reference to Segre's
Lectures on
Modern Geometry (1948, 1961).
(See Coxeter's reference 15
below.)
POSTSCRIPT
"It
is interesting to see
what happens…."
Another
thing that happens
if 1 + 1 = 0 —
It
is no longer true that
every finite reflection group
is a Coxeter group (provided we use Chevalley's
fixed-hyperplane
definition of "reflection").