Consider the people in simulation to be set of natural numbers and the stimulators to be set of even numbers, they will have the same cardinality but they won't be equal.sets (A) and (B) are both infinite and infinite countable sets are equal. The argument can't work if both sets are equal
I believe the best way to compare two infinite sets of same cardinality is by density measure, and the density of natural numbers will will greater as R ---> 100 such that f(a)=100 and as R--->100, even sets will have f(a)=50.The most straightforward way of making this notion precise in an infinite universe is via the idea of limit density. Start by picking an arbitrary spacetime point. Then consider a hypersphere centered on that point with radius R. Let f(A) be the fraction of all observations that are of kind A that takes place within this hypersphere. Then expand the sphere. Let the typicality of type-A observations be the limit of f(A) as R--->infinity.
I thought it was a rule that if infinite sets are countable, they're equal. No exceptions. — RogueAI
I believe the best way to compare two infinite sets of same cardinality is by density measure, — Wittgenstein
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