I searched invariant of a continuum as follows:




 I have assumed infinite possibilities of the analytical apparatus of the human – from the point of view of absence of restrictions from the mathematics party. I solved a problem with the bases for mathematics thus.

 I investigated various variants of continuums. I observed their properties by means of hearing, including an entropy gradient in a context of an arrow of time. I searched invariant of a continuum. It should be invariable for any continuums.

 I did not introduce axiomatics. I did not postulate concepts of space and time even.

 I searched a master key by method of selecting. I searched for the decision, but I have found it accidentally. We should consider the problem of the bases of irrational mathematics on the basis of this decision. I hear some phenomena and I do not find out them in the mathematics. But I hope for non trivial explanation of these phenomena by means of the found mathematical model.