Birth of Compound Numbers

Abstract

In this paper the author introduces a new kind of numbers called by 'Compound Numbers'. A region R may or may not have imaginary object. A region even may have more than one imaginary objects too. Corresponding to an imaginary object (if exists) of a region R, we get compound objects for the region R. Imaginary objects and compound objects of a region R are not members of R and so they are called imaginary with respect to the region R only (i.e. it is a local characteristics property with respect to the region concerned), as they could be core members of another region. Every region has its own set of imaginary numbers (if exist). As a particular instance, the compound objects of the set of real numbers are the complex numbers (of existing concept). In this paper the author discovers imaginary objects of the region C (the set of complex numbers). The compound objects of C are called by 'compound numbers'. Collection of all compound numbers is denoted by the set E. This work just reports the birth of compound numbers, not further details at this stage. It is claimed that Theory of Numbers will get a new direction by the birth of compound numbers. A new Theory of Objects' and the classical Theory of Numbers as a special case of it were also studied in (16). In this paper we say that every complete region has its own 'Theory of Numbers', where the classical 'theory of numbers' is just a special instance corresponding to a particular complete region RR. Consequently, we also introduce a new field called by Object Geometry of a complete region, being a generalization of our classical geometry of the existing style, from elementary to the higher level.