The decimal 0.(9) is referring to a 'completed' infinity. The most important question to be asked is this: Since you can't measure something with infinite accuracy, does infinity itself have a valid meaning in a purely mathematical concept?
This touches the idea that there can exist things in mathematics that do not DIRECTLY apply to anything in reality. I don't accept Ayn Rand basing ALL of mathematics on measurement. Rather I think that the mere notion of an entity as having an independent existence implies the notion of wholeness, or of something corresponding to an integer. Furthermore, math is purely deductive. It tells you, IF you take certain things as premises, where those premises lead.
So really what we should be asking is this: Is math any more fundamental than Ayn Rand's definition implies? If you have dealt with any advanced mathematics you have no choice but to consider infinity as something with some semblance of identity, and that contradict Ayn Rand's theory.
If someone closes this thread at least split this off. Everybody here is attacking method but nobody's actually going to convince anyone of anything by doing so.
Please consider my offer to start a new debate about where mathematics ACTUALLY fits into the world versus where Ayn Rand put it in her philosophy.
