Non-existance of function between equivalent left and right numbers

This paper is in the field of constructive mathematics, mainly discussing the existence of algorithmic functions between left and right numbers. A L (Left) number is any strictly increasing algorithmically given sequence of rational numbers bounded above by a bounding element θ ,which is a rational number. Two such numbers can be added in a natural way, but not be subtracted. One can also add a rational number and subtract a rational number from it. We can also assume that each rational number is naturally presented by some L number given as a geometric progression of rational numbers; R numbers are defined similarly. We showed there is no algorithmic map that maps a L number to an equivalent R number.