User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160725013617

One question and one observation:

How do you define the R function?

in order to know what the nth member of set K is, consider n is written in decimal, index the digits from right to left, call the rightmost digit i_0, the next one to the left i_1, the last one i_L then take let V_n be equal to their value, with the value of the first digit (from the right) being V_0, the value of the next digit to the left, is V_1, and so on till the value of the last digit V_L

nth member of set K ,

+(ω^i_L)V_L+(ω^i_L-1)V_L-1......+(ω^2)V_2+ωV_1+V_0

For example the 958724th set member is (ω^5)9+(ω^4)5+(ω^3)8+(ω^2)7+ω2+4

So the supremum of set K is ω^ω

By the way you only define the 1 argument f function yet later invoke f with two arguments, so this is ill defined