Confusion about a point and a line

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SUMMARY

The discussion centers on the philosophical implications of dimensionality in mathematics, specifically how a point, which has no dimension, can contribute to the formation of a line, which possesses dimension. Participants highlight the utility of redefining a point as an infinitesimal to navigate this conceptual confusion. The conversation emphasizes that while philosophical inquiries are intriguing, the mathematical framework is designed to provide clarity and utility. Additionally, references to Zeno's paradoxes are suggested for further exploration of these concepts.

PREREQUISITES
  • Understanding of basic geometric concepts, specifically points and lines.
  • Familiarity with infinitesimals in calculus.
  • Knowledge of Zeno's paradoxes and their implications in mathematics.
  • Basic grasp of mathematical philosophy and its relevance to mathematical definitions.
NEXT STEPS
  • Research the concept of infinitesimals in calculus and their applications.
  • Study Zeno's paradoxes to understand their impact on the philosophy of mathematics.
  • Explore the definitions and properties of points and lines in Euclidean geometry.
  • Investigate the philosophical implications of dimensionality in mathematics.
USEFUL FOR

Mathematicians, philosophy students, educators, and anyone interested in the foundational concepts of geometry and the philosophical questions surrounding mathematical definitions.

anhnha
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A point has no dimension and a line, which has dimension, is made from points together. How does something without dimension create something with dimension? I can't really make any sense of it. Could you share your opinions?
 
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Did you try searching for an answer online?
http://mathforum.org/library/drmath/view/55297.html
... note: this is strictly a point of philosophy concerning the nature of infinity.
You can get around it by redefining a point as an infinitesimal.

As far as this forum is concerned (we don't do philosophy here) the study of mathematics has been arranged so these rules make sense and are useful. Just treat it as a definition.
 
Yes, I searched a lot but still feel confused. I am doing some integrals and really curious.
You can get around it by redefining a point as an infinitesimal.
That makes sense.
Is there an direct explanation to this even philosophy?
 
Is there an direct explanation to this even philosophy?
See the link. Also research Xenos paradoxes.
The questions are that old.
 

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