Abstract :
This study investigated the method of integrating positive integer number types while keeping the amounts of them being traced. It distinguishes from most current adopted definitions and researches which deal with the two aspects independently. An integrated evolutional cognition model of integer numbers is depicted in the manner of a number version "cosmos explosion" (NCE). By providing a tunnel to repeat a formation/creation process of numbers, NCE allows not only a new systemic view on semantics/definitions of {numbers, number types, relationships among them}, but also opportunities to retrospect on some of the fundamental/historical issues related to the understanding of numbers. To illustrate the number classification and locating functionalities of NCE, some examples are shown related to the locating of prime numbers, and deduction on the amount and composition relationships among number types, etc, in the "explosion" processes of NCE. NCE is promising to be extended to areas of number theory, semantics, computation, cryptology, modeling, etc.
