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A novel software implementation of set theoretic relations and operations.

IP.com Disclosure Number: IPCOM000016018D
Original Publication Date: 2002-Jan-30
Included in the Prior Art Database: 2003-Jun-21
Document File: 4 page(s) / 87K

IBM

Abstract

Introduction A novel software implementation of set theoretic relations and operations is presented. The novelty lies in assigning to each element in a finite set a unique prime number, calculating a set coefficient for the set, and using the set coefficient and the assigned prime numbers in arithmetic operations to implement set theoretic operations and relations on the set. The main advantage with the method is that the entire set is captured in an encoded form in a single number, the set coefficient. Let x 1 , x 2 , . . ., x n represent the n elements of a finite set A . This is usually stated as A x 1 , x 2 , . . ., x n }. It is assumed that no two elements in the set are identical. Therefore the cardinal number for the set A is n . The ordering of the elements inside the curly brackets has no significance. When we write s • S it means that the element s belongs to the set S .