before_revision: Our goal is to construct mathematical operations that combine non-determinism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the objective is for the operations to preserve bi-immunity. While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the  symmetric group on the natural numbers. The structure of this new subgroup  is unknown.
after_revision: Our goal is to construct mathematical operations that combine indeterminism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the operations preserve bi-immunity. While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group on the natural numbers. We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive. The complete structure of this new subgroup and its subgroups generated by one or more bi-immune rearrangements is unknown.
edit_actions: R
edit_actions: non-determinism
edit_actions: indeterminism
edit_actions: fluency
edit_actions: clarity fluency fluency
edit_actions: R
edit_actions: objective is for the operations to
edit_actions: operations
edit_actions: clarity
edit_actions: clarity clarity clarity
edit_actions: A
edit_actions: infinite
edit_actions: meaning-changed
edit_actions: meaning-changed meaning-changed clarity
edit_actions: R
edit_actions: The
edit_actions: We show that this new subgroup contains the bounded symmetric group on the natural numbers, and consequently is highly transitive. The complete
edit_actions: meaning-changed
edit_actions: meaning-changed meaning-changed meaning-changed
edit_actions: A
edit_actions: and its subgroups generated by one or more bi-immune rearrangements
edit_actions: meaning-changed
edit_actions: meaning-changed meaning-changed clarity