My point was that .999=1 is a direct result from the fact that the number line is continuas.
Imagine that you had a number system which does have holes in it (for example, the difference between .999... and 1). Now, take 2 object, one at mass .999..., and the other one of mass 1. In this hypothetical system, these objects would have a different mass. Now, take a third object, whose mass is between the 2 of them.
I consider it a critical property of our number system that we can be guaranteed to have a number representing the third mass.
As a historic note, the Greeks believed that any 2 numbers could be expressed as a multiple of some unit. For example 2 and .333... could both be expressed as multiples of 1/3. Eventually, they proved that this system could not accuratly moddel their world (the diagonal of a square for example).
I suspect that if we did have a number system such as you described, we would eventually discover that it did not work well enough for us, and switch to a continuas one.
Imagine that you had a number system which does have holes in it (for example, the difference between .999... and 1). Now, take 2 object, one at mass .999..., and the other one of mass 1. In this hypothetical system, these objects would have a different mass. Now, take a third object, whose mass is between the 2 of them.
I consider it a critical property of our number system that we can be guaranteed to have a number representing the third mass.
As a historic note, the Greeks believed that any 2 numbers could be expressed as a multiple of some unit. For example 2 and .333... could both be expressed as multiples of 1/3. Eventually, they proved that this system could not accuratly moddel their world (the diagonal of a square for example).
I suspect that if we did have a number system such as you described, we would eventually discover that it did not work well enough for us, and switch to a continuas one.