User blog:Sigmafive/SF Function

SF is a multivariable natural number function I invented focused strongly on diagonalization whenever possible and recursion.

so far I think its about as powerfull as chained arrow notation (maybe more) but I need to do an analysis to go to any conclusion.

here is its definition

SF(x) = x+1 (or even any single variable function you want)

any trailing 1's are removed accept for single input

ex1: SF(3,4,1,1,1) -> SF(3,4)

ex2: SF(1) -> SF(1)

SF(a,b,...) = SF(SF(a,1,...),b-1,...) | if b > 1

ex: SF(4,3,6,4) -> SF( SF(4,1,6,4),2,6,4 )

SF(a,1,..(n 1's)...x1,x2,x3...) = SF(a,a,...(n a's)...(x1-1),x2,x3...)

ex1: SF(3,1,2) -> SF(3,3,1) -> SF(3,3)

ex2: SF(a,1,1,1,4,7,6) -> SF(a,a,a,a,3,7,6)

more examples

SF(5,6) -> SF(SF(5,1),5) ->  SF(SF(5),5) ->> 11

SF(a,b) is the same as a+b

sorry if these rules are vague but just point anything out that needs clarification