Recent content by velikh

As it is not difficult to notice, the first of these two sums ##N = b_ob_1b_2b_3. . . b_i## increases very slowly. While the second of these two sums ##[x] = R## alternately changes either increases or decreases. Further, patterns of the change in the first sum ##N## are obvious and do not...

$$x=b_0b_1\dots b_{i-1}b_i=1110101\dots 01$$

Before that I did not work with binary system of calculus. Nevertheless, if I understand correctly, namely: $$63 = 111111$$ $$43 = 101011 = 31 + 12 = 11111 + [1100] := N + [x]$$ $$31 = 11111$$ $$20 = 10100 = 15 + 5 = 1111 + [101] := N + [x]$$ However, I do not quite understand how it is possible...

Thank you very much for your participation and the questions asked. I will try, as far as possible, to explain some perhaps controversial definitions. The fact is that ##x## and ##y## are not power series. However, ##x## and ##y## are positive integers that can be considered as partial sums of...

Let (x, y) be some arbitrary positive integers such that: $$x:=\sum_{n=0}^kq2^n, ~~~ y:=\sum_{n=0}^{k+1}q2^n, ~~~\text{where: q = (1, 2), k = (0, 1, 2, 3, . . ., n).}$$ For example: $$x:=[2^0+2^1+2^2+2^3+(2^3)]= 23, ~~~\text{where:} ~~~\sum_{n=0}^x(q-1)2^n = 2^3,$$...

Then maybe like this: $$[a]:= \sum_{n=0}^x (q-1) 2^n :=2^3$$ Although I still need to think. Sincerely thank

Let (a, b, c) be some arbitrary positive integers such that: $$a:= \sum_{n=0}^x q2^n , ~~~~~ b:= \sum_{n=0}^y q2^n , ~~~~~ c:= \sum_{n=0}^z q2^n, $$ where: $$q = (1, 2), ~~~(x, y, z) = (1, 2, 3, . . ., n). $$ For example: $$a:=23=[2^0+2^1+2^2+2^3+(2^3)],$$ where: $$\Delta{a}:=2^3,$$...

Let (a, b, c) be some arbitrary positive integers such that: (q2^0 + q2^1+ . . . + q2^x), (q2^0 + q2^1+ . . . + q2^y), (q2^0 + q2^1 + . . . + q2^z), where: q = (1, 2), (x, y, z) = (1, 2, 3, . . ., n). In the case if and only if q = 2, we accept the following notation : [(q-1)2^0...