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)

>>10
The point is that if something's wrong in mathematics, you take issue with the axioms and not the theorems.  If the Banach-Tarski theorem was not enough for the average mathematician to throw out the axiom of choice, then surely a schoolchild's opinion that .999... should not be equal to one is not enough justification for the reformulation of our entire system of arithmetic.
It's pretty obvious that the person who developed this terminology 1-6 (probably OP himself) is not a mathematician, because not only do the descriptions have no rigor to their distinctions, but the question is equivalent to saying "What is your stance on this arithmetical theorem that has been proven true in standard arithmetic?"  An actual mathematician might ask "What is your stance on axiom A", or "What is your stance on unproved conjecture B", but asking for a stance on a theorem is pure lunacy.