[FOM] Question on the number line  Dean Buckner d3uckner at
btinternet.com Tue Nov 15 15:34:49 EST 2005  Forgive me if this
is a naïve question.  It occurs in the chapter in Suarez (the
16C philosopher & mathematician) that I mentioned in a previous
posting.  Suppose one takes a line segment of length 1 and break
it in half (assuming we can break it "in half").  Intuitively,
you would imagine you get two identical segments of length 0.5.
But if you "identify" that line segment with the reals from 0.0
to 1.0, you have to ask what happens to the point at 0.5 --
which "half" does it belong to?  If it stays with only one side,
then you don't have two identical line segments.  Instead, you
have one segment that is closed at both ends and another segment
that is open at one end.    Suarez discusses a wall, originally
all one colour, half of which has now been painted another
colour.  Which colour is the boundary between the one colour and
the other?  It can't be both colours.  To resolve the problem he
distinguish