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Definition 2.5.1: A distribution of an attribute is totally chaotic if the assignment relations do not have any invariance domain, and the domain of the distributed and of the support attribute are continuous and infinite.
Comment 2.5.1: The distribution type was not mentioned any more in definition 2.5.1 (primary or derived distribution) because the definition is valid for both distributions types. When only the “distribution” term shall be used next in this paper, this means that any of its types are self-understood.
According to the definition 2.5.1, a totally chaotic distribution is a particular case of distribution, where there is not a single continuity interval across the entire support domain, for the assignment relations, the allotted values being totally random. The totally chaotic distributions may be also probabilistically defined, which means that these are the distributions at which the density of occurrence probability of any value is even (equiprobable values). After all the facts which have been aforementioned in this paper, it is obvious that the totally chaotic distributions are virtual objects, used in mathematics field, but unable to be realized. If the values domain of the distributed and support attribute is limited (finite and known), made-up from a finite number of normal singular values, then the distribution is only partial chaotic (that is the case of realizable chaotic distributions) and that is due to the fact that any restriction on a domain of values means a information amount growth, as we are about to see in chapter 8 and 9. In case of the totally chaotic distributions, the inner information amount associated to them is null.
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