Classify the equivalences of infinite paths down Pascal's triangle
Infinite paths down Pascal's triangle
Two paths on Pascal's triangle are equivalent if they lead to the same spot. Equivalently, two different noncommutative terms are equivalent if they are the same upon introducing commutativity. When the paths are infinite than either one is a finite number of moves to the left or right and so these can be matched; or there is an infinite number of moves on either side. We can consider if there is an algorithm to equate them. Thus this is a context for a topology of commutativity.