/-Existence

Abstract

In Section 11–1, as part of a general discussion, we introduced the notion of /-existence as a formal device for avoiding the use of products in which −∞ and +∞ are combined. Generalising this notion, let E_l be a belt with duality having a trisection (σ_−∞, σ_ø, σ_+∞), and let x,yεE_l. We shall say that the products x⊗y and x⊗′y are /-undefined.if one of x,y lies in σ_−∞ whilst the other lies in σ_+∞ Similarly, we shall say that a matrix product, or other expression, is /-undefined if its evaluation requires the formation of a/-undefined product of elements of E_l. Otherwise, we shall say that such expressions or products are /-defined or that they /-exist.