PUZZLaTOMictM

The number family above falls from top to bottom or rises from bottom to top.

It falls as follows:

Octonions can produce

Quaternions can produce

Complex Numbers can produce

Real Numbers can produce

Rational numbers can produce

Integers can produce

Natural numbers with zero then

Natural numbers with no zero

Hovering above and meandering around and through all these simple quantity
numbers are the infinities or Alephs of Cantor (uses the Hebrew symbol for N, N0
being the set of natural numbers number fields while N1 is
thought to be the set of real numbers. These infinite numbers go on
forever and have a whole hierarchy of infinite numbers many infinities upon
infinites larger. There are also new concepts (relatively speaking!!) such as
algebraic numbers, and other things that can be thought of simply as kinds of
numbers such as limits, series, Zeta function of Riemann, Prime types, the list
is much larger and always growing. It is a big field but still a perfectly
manageable thing and a beautiful machine of great power. Without this growing
mathematical machine future and present technology would probably eventually
come to a screeching halt!

Perhaps someday we will have a computer that we can pose mathematical questions
to, and by asking just the right questions, very creative and inspired
questions, the computer will go to work and out will come wonderful new
mathematics from time to time!!

Copyright 2013 © by Douglas A. Engel, Littleton, CO, U.S.A.