i guess the thing i'm disagreeing on relates to a definition of a surface that requires discrete or compositional elements to describe.
a point is before a set, a set is a collection of points. a line can be divided, then you can make a set, a set could be said to be all sets of points in a single dimension. you can make that dimension infinite, or you can make it circular, again, the geometry precedes the establishment of a set.
a point is the primary unit of topology. so i guess i'm splitting hairs.
i just don't agree with the post-hoc nature of sets, being primordial compared to the ad-hoc nature of divisions of surfaces.
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Follow most of your line of reasoning. Agree to disagree slightly 🤷♂️
yeah, correcting myself. the topology precedes the set.
a circle, as in a theoretical perfect circle in a continuous (real) field is not an infinite set of points. that is an approximation of a circle, just as you can't get a precise number, in any number base, for the ratio of circumference to radius.