First let us examine a well-known relation between mathematical objects and their representations.

=>> is ‘represented by’

|{}|=>>0 ; |{{}}|=>>|{0}|=>>1 ; |{{},{{}}}|=>>|{0,{0}}|=>>|{0,1}|=>>2 ;

|{{},{{},{{}}}}|=>>|{0,{0,{0}}}|=>>|{0,1,2}|=>>3 ; …

Let us see how we use my method to construct a collection of R members.

R members are constructed like this:

1) First let us examine how we represent a number by my system:

=>> is ‘represented by’

a) |{}|=>>0

b) There is 1-1 and onto between ‘0’ and the left edge of {._.} and we get {‘0’_.}

c) |{{}}|=>>|{0}|=>>1

e) There is 1-1 and onto between ‘1’ and the right edge of {._.} and we get {‘0’_’1’}

In short, {.} is the initial place of R collection, which is represented by ‘0’, where {‘0’_.} is the initial place of the second place of R collection, which is represented by ‘1’, and we get our first two must-have building-blocks of R collection.

2) When we get {‘0’_’1’} we have our two must-have numbers, which are ‘0’
and _’1’. Be aware that ‘0’ is the representation of {.} where ‘1’ is the representation of {._.}.

3) If we get {.}_AND_{._.}, then and only then we have the minimal must-have information to construct the entire R collection because:

a) We have ‘0’ AND _’1’ that give us the to basic scale factors 0 and _1.

b) We also have our initial domain _1, which stands at the basis of any arbitrary scale factor that is determined by the ratio between the initial domain _1 and another segment, which is smaller or greater than the initial domain _1 , for example:

0 = .

1 = 0__1

2 = 0____2

3 = 0______3

.5 = 0_.5

0_________pi

The negative numbers are the left mirror image of the above numbers.

There is no division in my number system because both {.} and {._.} are indivisible by definition.

In short, any segment is an independent element that clearly can be shown in the above 2-D representation.

If we use a 1-D representation, we get the standard Real-line representation, but then we can understand that division is only an illusion of an overlap of independent elements when they are put on top of each other in a 1-D representation,
for example:

0_.5__1_____2_____3__pi

Since in my system nothing is divisible, then '/' stands for a ratio between at least any given two (indivisible) numbers.

oo=|{___}|

0=|{}|

0__pi

(x-pi)(x-sqrt(2))

anxn + an−1xn−1 + ··· + a1x + a0 = 0