08-14-2015, 04:37 AM
(08-14-2015, 03:41 AM)Shaadaris Wrote: PREPARE FOR HEAD EXPLODE.
Part of this is the paradox as such, in simpler terms:
Take an object, and break it down into infinite pieces. Putting those pieces back together ends up with... two objects.
Let's set aside the fact that subatomic particles may stop somewhere at some size (if they ever do).
This paradox is set on a few axioms. Axioms are things about the world which we must take for granted. We base our science upon them, but axioms are un-provable. This paradox is set on many axioms that are well-respected, except for one:
The axiom of choice. The axiom of choice states, that, in the classical probability experiment, we have two buckets with some objects in them, and we may take them out, but when taking out objects, we have taken out exactly one object from each bin (this is a a massive simplification of what really happens, by the way). This axiom must be true for the paradox to work correctly.
Before, the axiom of choice was controversial. But today, due to it being used in several, accepted mathematical results, it no longer is. But we might never know how the world really works, and the paradox may yet go untested.
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