Sets have open or closed boundaries {boundary, set}. Actions can create a boundary {expansion, laws of form} or cross a boundary {contraction, laws of form}. Complex actions combine expansions and contractions.
marking
Boundary side can be positive {marked region} and other side negative {unmarked region}.
space
Drawing boundary inside space tells nothing about whole space. Encircling whole space with boundary tells nothing about whole space.
boundary making
Interaction between observer and system {boundary making} makes larger system containing both observer and original system. Observer can surround all or some sets or be inside a set in the set hierarchy.
Observer cannot know whole system, only part close to boundary. Observer makes boundaries to describe whole system.
interval
Regions {interval, laws of form} have boundaries. Boundaries can be in marked sets or spaces {open interval, set}. Boundaries can not be in marked sets or spaces {closed interval, set}.
operations at boundaries
Going from inside boundary to outside boundary is opposite operation {inverse, laws of form}. Going from inside boundary to outside boundary, and then going from inside boundary to outside boundary, results in original condition {identity, laws of form}. Drawing same boundary second time is NULL operation and gives no new information.
Mathematical Sciences>Set Theory>Laws Of Form
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Date Modified: 2022.0224