The article introduces a three-character Markov representation of numbers, which is \\ based on the decomposition of a number into a series
x=α1−1∑i=0qi+∞∑k=1(qα1αk−1∑i=0qαkik−1∏j=1qαjαj+1)=Δα1α2...αk...,αk∈A={0,1,2},x=∑i=0α1−1qi+∑k=1∞(qα1∑i=0αk−1qαki∏j=1k−1qαjαj+1)=Δα1α2...αk...,αk∈A={0,1,2},
where $\|q_{ij}\|$ --- a positive stochastic matrix (transition matrix probabilities), $(q_0;q_1;q_2)$ --- a positive stochastic vector. This representation is a generalization of the classical ternary representation of numbers and coincides with it for $q_i=\frac{1}{3}=q_{ij}$ $\forall i,j\in A$. The topological-metric properties of the cylinders of the Markov representation are described, in particular, the basic metric \\ ratio of the lengths of the cylinders of the previous and next ranks is written out. The concept of \\ Markov-normal number is introduced and it is proved that the set of numbers, the asymptotic frequency of each digit $i$ of which is respectively equal to $\sum\limits_{i\in A}q_jq_{ji}$, $i,j\in A$, has a full Lebesgue measure.
The function (inverter of numbers) is introduced, defined by the equality
I(x=Δα1α2...αn...)=Δ[2−α1][2−α2]...[2−αn]....I(x=Δα1α2...αn...)=Δ[2−α1][2−α2]...[2−αn]....
It is proved that the function $I$ is a continuous strictly decreasing function on the interval $[0;1]$. Based on the concept of a cylindrical derivative, an expression for the derivative of the function $I$ at a point is found. \\ Using the normal property of a number by its Markov representation and \\ the obtained expression for the derivative, conditions for the derivative to be zero at almost every point of the unit interval in the sense of the Lebesgue measure, i.e. conditions for the singularity of the function $I$, are found.

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