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Classify the equivalences of infinite paths down Pascal's triangle
- How are infinite paths down Pascal's triangle the basis for analysis?
- What is the relationship between algebra and analysis?
- What is the role of commutativity and equivalence?
- What is the relationship with Taylor series?
- What kind of relationship is there between the two ends of an infinite sequence, the beginning and the lack of end?
- What does the usual order of the reals mean here?
- What do derivative and integral mean here?
- What do computable functions mean here?
- What is the division of everything in terms of differentiating the Taylor sequence?
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.