I have a question probably related to pure mathematics, but I'm not sure. I have some line segments (in 1-dimensional space), where I want to define a function over them to make a union of them. However, my definition of union means a new line segment starting from the minimum position between line segments, and finishing at the maximum position of end positions between line segments. Is there any algebra where some operator (for example + or $\cup$) in it satisfies my requirement.
Algebra over line segments
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linear-algebra
algebraic-geometry