0.999... Poll

What is your stance on this Paradox(0.999... repeating decimal and its value)
1.Transformatism(1 is exactly the same number as 0.999... written in different form)
2.Strong Convergism(1 is equal to 0.999... in all aspects)
3.Weak Convergism(0.999... converges to 1 at infinity)
4.Weak dualism(1 is equal to 0.999... practically, but is different in exact values)
5.Strong Dualism(1 is different and inequal number to 0.999...)
6.Separatism(1 and 0.999... belong to different number classes and cannot be compared)

>>13
Traditionally, a real number is defined as either a Dedekind Cut or a Cauchy sequence of rationals (defined from equivalence classes of pairs of integers, defined from equivalence classes of pairs of finite ordinals), wherein the theories of real analysis take hold.  I would be very interested to see an alternate definition of a real number where you could see a distinction between the two.  Do you have a source?