The integration operator has a pole at *Z* = 1, which
is exactly on the **unit circle** |*Z*|=1.
The implied zero division has paradoxical implications
(page )
that are easy to avoid
by introducing a small positive number and defining .The integration operator becomes

(23) | ||

(24) |

Figure 4

Just for fun I put random noise into an integrator
to see an economic simulation,
shown in Figure 5.
With , the difference between today's price
and tomorrow's price is a random number.
Thus the future price cannot be predicted from the past.
This curve is called a ``**random walk**."

Figure 5

10/21/1998