On Cantorian spacetime over number systems with division by zero

Division by zero is proposed in order to open new horizons for abstract mathematics and physics. Although the formerly forbidden operation may be of little practical value, the feasibility of unrestricted operations is needed for meaningful deployment of linear vector spaces, whose duals are inverse transposes of their primary vector spaces. Both quantum mechanics and pan-geometry of multispatial hyperspace operate on vectors that belong to mutually dual linear vector spaces. The division by zero also may remove many years old paradox related to multiplication of zeros and makes it possible to introduce the concept of bigroup as an additive and multiplicative group at the same time. This operational extension to algebraic groups makes thus an infinite-dimensional, fractal Cantorian spacetime the preferred, invertible, operationally unrestricted, abstract mathematical infrastructure for physics. (C) 2003 Elsevier Ltd. All rights reserved.