Removing parts of a line (literally)

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SUMMARY

This discussion focuses on the properties of line segments, specifically the effects of removing parts of a segment on its length and endpoints. It clarifies that an open line segment excludes endpoints A and B, while a closed segment includes both. The discussion also distinguishes between half-open segments, which include one endpoint but not the other. Importantly, the inclusion or exclusion of endpoints does not affect the overall length of the segment.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly line segments.
  • Familiarity with open, closed, and half-open intervals.
  • Knowledge of mathematical notation for intervals, such as [0,1] and (0,1).
  • Basic comprehension of length measurement in geometry.
NEXT STEPS
  • Explore the properties of open and closed intervals in real analysis.
  • Learn about the implications of endpoint inclusion in mathematical contexts.
  • Investigate the concept of measure theory and its relation to length.
  • Study the differences between finite and infinite intervals in geometry.
USEFUL FOR

Mathematicians, geometry students, educators, and anyone interested in the foundational concepts of line segments and interval notation.

member 428835
Hey pf!

I think this is the correct thread. Basically, if I take a line segment and remove half of it, what happens to the point that is in the middle?

Also, what happens if I take a segment [0,1] and take [0,1/2) versus [0,1/2]? What length do I have remaining for each of these?

Thanks!
 
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If you define a line segment as the points between points A and B, but excluding A and B, it is an open line segment. If it contains both A and B, it is a closed segment. If it includes one but not the other, it is call half-open.

The inclusion or exclusion of the endpoint does not affect the length of the segment.
 

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