Infinity

We often get around judging others through actions by pointing out that we all have flaws and our own personal struggles.  Some may be more evident than others but it's about a direction and a goal more than a measure of current position.  All well and good but it underlies that common belief that actions are good or bad: definable; as well as the truth that when perfection is reached our actions will be limited to only the Godlike actions.

Let us class these actions together as a set of all possible actions for those who have achieved perfection.  Then let us create a set of all actions an eternal individual takes from the moment perfection is reached ("the perfect day").  This latter set must be infinite as the actor is infinite, so we have one infinite set containing a series of subsets of actions. Now let us write out each possible 'god-action' as a string of digits.  However many it takes is irrelevant as long as it's finite.  Some unique code of digits, even hundreds of digits long, will be used in place of an English descriptions.  Now we know from infinite set theory that the set of numbers which  do not contain every possible, arbitrary finite set of numbers has measure zero.  Or a zero probability that any number selected from the infinite set of numbers (real numbers, thus including the irrational) wont contain every possible number set.  Or to simplify once more, than there's a hundred percent chance that any number chosen will contain every possible combination of digits.

Combining this knowledge with our original set-up we write out the set of all actions taken by an eternal being as a string of digits which represent their actions.  This being an infinite number, there is now a hundred percent chance that it contains any arbitrary set of of actions within it (all in the subset of 'god-like').  Thus no actions of any other being can be unique in any way.  Instead it is provable that all actions taken by all other beings are a subset of those actions taken by this being, thus rendering all others redundant.  Not very happy, right?  The only escape being if the set of measure zero contains all actions of these beings which would require endless repetition thus moving the redundancy from other beings into the self.  If we can not be mere replicas of other eternal beings then we are doomed to self-repetition and become ourselves redundant.  What is the solution?  Or are we truly redundant, and thus without necessity or purpose?

There are two assumptions made which may not be correct to arrive at that proof, can you find them?

Here's something to think about:
Even if both assumptions are wrong it is still provable that all positive (above called 'god-like') actions we perform in this life are redundant if we become eternal beings.  Unless our actions are not truly good, gods do not perform good acts, or gods are not eternal any arbitrary, finite set of actions (such as that set we perform here on earth) will be found in the infinite set of actions we perform after the resurrection.  In fact, at some point, they must be performed in the same order as we performed them here on Earth!