> Axiom of choice assumes that you can always pick the best possible option, however you need to be able to account for your worst possible options as well. All mathematical optimization falls outside of classical logic.
Not sure what you mean here. The axiom of choice just says that the Cartesian product of a set of nonempty sets is nonempty. Can you explain what you mean by "best possible option" and "worst possible options"?
With regards to (2), this is one way of solving the problem. However, your solution uses O(n) memory (where n is the size of the linked list), and the tortoise-and-hare algorithm uses only O(1) memory. Here's how it works: http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_ha...