Abstract: Focuses on the ability of physical objects to the issuance of some material substrate
(photons, electrons, etc.), which provides formation of the real reflections of the external world objects
not only in computer's memory, but also in the environment, in all elements of electronically or optical
machines parts. Here proposed the concept of elementary material reflections carriers - static and
dynamic Ixelles. The initial state of Ixelles shape-images of physical prototype objects are considered
as informational substance - the basis of the subsequent formation of information objects hierarchy.
Reviewed two mathematics paradigms, differs in origination source and essence of mathematical
objects: a mental paradigm, the original concepts, axioms, concepts of which are offered by
mathematicians and agreed with the structure of human mind, and the machine paradigm, the original
ideas, concepts, methods are inputted by computer science developers based on chosen mechanisms
of formation and information objects processing technology.
Keywords: object, reflection, Ixel, info substance, machine mathematics
FROM REALITY TO THE OBJECTS OF COMPUTERS SCIENCE AND MATHEMATICS