4. COGNITIVE VISUALIZATION
OF CONTINUUM PROBLEM
"Transfinite Numbers themselves are, in a certain sense, new irrationalities. Indeed, in my opinion, the method for the definition of finite irrational numbers is quite analogous, I can say, is the same one as my method for introducing transfinite numbers. It can be certainly said: transfinite numbers stand and fall together with finite irrational numbers."
 Georg Cantor.
Denote the tree in Fig. 1 by T_{R},
rotate the tree T_{R} counterclockwise at 90°
and place a mirror AB at its root V in parallel to its levels. The visual result
of such transformation we can see in Fig. 2, that
demonstrates a CognitiveVisual image of the mirrorlike
11correspodence, say Y,
between the initial tree T_{R}
and its mirror image  the tree T_{L}.
The interpretation of the levels of the trees T_{R}
and T_{L} is also given in Fig. 2.
Fig. 2. Cognitive Visualization of Continuum Problem and the hyperreal numbers system:
a) level numbers of the trees;
b) powers of the base 2 in the binary system;
c) binary representation of the "inbothside transfinite" hyperreal numbers.
