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The set of ordered sets is a subset of the set of sets. Totally ordered sets, which I think are synonymous with chains(?), are still sets.

But yes, I was talking loosely: my point was to differentiate between a mental model of iterating over a sequence (or ordered set) and applying a set-like transformation. My mental picture was of a field formed by a matrix operation on a limited space as being composed of the summation of a series of vector transformations; my maths language doesn't really allow me to properly describe it however. Loosely: you can break down a [subset of] 3D transformation[s] of a surface in to a series of 2D transformations performed iteratively, or you can apply a 3D transformation; they're different mental images of acquiring the same result.




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