@article{tjant2014264,
author={Biswas, Ranjit},
title={Birth of Compound Numbers},
journal={Turkish Journal of Analysis and Number Theory},
volume={2},
number={6},
pages={208--219},
year={2014},
url={http://pubs.sciepub.com/tjant/2/6/4},
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 . 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.},
doi={10.12691/tjant-2-6-4}
publisher={Science and Education Publishing}
}