**Cantor's
image** is
flanked
by the
"**Aleph**",
the first
letter
of the
Hebrew
alphabet,
which Cantor
used (accompanied
by subscripts)
in his
descriptions
of *transfinite* numbers
-- quite
simply
numbers
which were
*not
finite.*
Cantor
recognized
and demonstrated
that infinite
sets can
be of different
sizes. He
distinguished
between
countable
and uncountable
sets, and
was able
to prove
that the
set of
all *rational
numbers* **Q** is
countable,
while the
set off
all *real
numbers* **R** is
uncountable,
and therefore,
though
both were
infinite, **R** was
strictly
larger. Backing
Cantor's
image is
a graphic
generated
from a
"**Cantor
Set**".
A "**Cantor
Set**" is
an **infinite
set** constructed
using *only* the
numbers
between** ***0* and **1**.
A Cantor
set is
constructed
by starting
with a
line of
length
1, and
removing
the middle
1/3. Next,
the middle
1/3 of
each of
the pieces
that are
left are
removed,
and then
the
middle
1/3 of
the pieces
that remain
after that
are removed.
The set
that remains
after continuing
this process
forever
is called
the Cantor
set.
The
Cantor
set contains
uncountably
many
points.
**The
graphic
**set
which
backs
Cantor's
image
began
with
an algorithm
to
generate
the
Cantor
set,
to which
color
was applied,
and then
universal
operators
related
to color
transition
and magnification,
ultimately
resulting
in a
unique
image
whose
essence
was the
Cantor
set.
**The
final
problem **which
Cantor
grappled
with
was
the
realization
that
there
could
be
no
set
containing
*everything*,
since,
given
any
set,
there
is
always
a larger
set
--
its
set
of
subsets.
Cantor
came
came
to the
conclusion
that
the ** Absolute** was
beyond
man's
reach,
and identified
this
concept
with
**God.**
In one
of his
last
letters
Cantor
wrote:
I
have
never
proceeded
from
any
'Genus
supermum'
of
the
actual
infinite.
Quite
the
contrary,
I have
rigorously
proved
that
there
is
absolutely
no
"Genus
supremum'
of
the
actual
infinite.
What
surpasses
all
that
is
finite
and
transfinite
is
no
'Genus';
it
is
the
single,
completely
individual
unity
in
which
everything
is
included,
which
includes
the **Absolute**,
incomprehensible
to
the
human
understanding.
This
is
the
*Actus
Purissimus*,
which
by
many
is
called
**God**."
- Georg
Cantor |