Presupposition - All points of a longer (the infinite form) can be replaced with labels: (0), (0,1 ),...,

(0,1,2,3,4,5,6,7,8,9 ),...

Process:

P_{1}-N (_{0}) = {0,00,000,0000,...}

P_{2}-N (_{0,1}) = {0,1,10,11,100,...}

...

P_{10}-N (_{0,1,2,3,4,5,6,7,8,9}) = {0,1,2,3,4,5,6,7,8,9,10,11, ...}

...

--a3--

[S_{4}]-number along

[S_{5}]-set of natural numbers N

We will use N (_{0,1,2,3,4,5,6,7,8,9}) = {0,1,2,3,4,5,6,7,8,9,10,11,12,...}

Definition[number along]- a starting point (0), the last point at infinity

[number N]-The number 0 is the point 0

-Other numbers are longer, the first item is 0, the last point is the point of the name (number)

CM-[S_{4}].does not know , [S_{5}]-axiom