Hello, Kodt, you wrote: V>> As wrote already nearby, seemingly, that any total fusible numbers as "the necessary mandatory minimum" expresses through "mandatory" application of the formula (x+y+1)/2, calculating. That is, seemingly, that join generally all (arbitrary) mn-in, satisfying to a condition, will coincide with minimum or to be its subset. How it - "join of all" will be a subset minimum?! I will try to explain. Is certain f-ija which postulates presence of certain elements in mn-ve since she says that if p and q - elements mn-va and distance / them <1 x=F (p, q) - too the element of it mn-va. It is Still given that 0 is an element of it mn-va, we accept x 0=0. Total, substituting x 0 in F, we receive: x 0:1 = F (x 0, x 0). Further: x 0:2 = F (x 0, x 0:1). x 0:3 = F (x 0, x 0:2). x 1:2 = F (x 0:1, x 0:1). x 1:3 = F (x 0:1, x 0:2). Etc. I.e. It is necessary to apply mutually F to all available and received on each step x i and x j, the distance / with which is less 1. Received mn-in I nearby named "a mandatory minimum", i.e. it and is required minimum mn-in. We argue further. We present that it is possible to take the arbitrary number r, "violently" to include it in mn-in and as mutually under the formula still elements such mn-va. And so, if r is not the number received under the initial recurrence formula we in what "minimum mandatory", APPRX. Simply I stated that any number, representable in the form of the total of elements x i from minimum mn-va, too is included in the magic image into it mn-in. For example: x 0:1+x 0:1=1/2+1/2=1. And the limit of some x 0:n, n-> oo too is equal 1. Still: x 0:1+x 0:2=1/2+3/4=5/4. The limit of some x 1:n, n-> oo too is equal 5/4. Etc. Further. There are still such observations: For any number of a type 2-x 0:n is mandatory there will be a row from this the most minimum mn-va, converging to this number. For example: 2 - 1/2 = 3/2 - there is such row. 2 - 3/4 = 5/4 - there is such row. 2 - 7/8 = 9/8 - there is such row. 2 - x 0:n, n-> oo = x 0:n, n-> oo = 1 2 - 0 = x 3:n, n-> oo = 2 And it is for some reason true for any number r> = 2. ., any number r> = 2, at first, in the form of the total of elements x from minimum mn-va 1/2 <= x <= 3/2, in the second, too is included into this minimum mn-in at its recurrence calculation. Total, for numbers from a range 1/2. 1 it is enough to learn on an accessory to a row: 1/2 3/4, 7/8..., 1-2-nCHto it is elementary, if a rational number to present in the form of natural fraction. And here for numbers from a range 1. 2 it is "enough" to learn on an accessory to one of rows: 1. 1/2+3/2-1/2 1/2+3/2-3/4, 1/2+3/2-7/8... 1/2+5/4-1/2 1/2+5/4-3/4, 1/2+5/4-7/8... 1/2+9/8-1/2 1/2+9/8-3/4, 1/2+9/8-7/8...... 2. 3/4+3/2-1/2 3/4+3/2-3/4, 3/4+3/2-7/8... 3/4+5/4-1/2 3/4+5/4-3/4, 3/4+5/4-7/8...... 3. 7/8+3/2-1/2 7/8+3/2-3/4, 7/8+3/2-7/8... n.... Meanwhile there is an observation that in diagonals of everyone n- matrixes contain identical numbers, i.e. it is possible to replace each of them with its any column or a line. Total, the group of matrixes is degenerated in one matrix the accessory to which should be found... ==== it is interesting, and the HARDWARE has a decision?))