Confusion about a point and a line

  • Context: High School 
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Discussion Overview

The discussion revolves around the conceptual relationship between points and lines in mathematics, particularly focusing on the dimensionality of points (having no dimension) and lines (having dimension). Participants express confusion about how a dimensionless entity can contribute to the formation of a dimensional one, with references to philosophical implications and mathematical definitions.

Discussion Character

  • Conceptual clarification, Debate/contested, Meta-discussion

Main Points Raised

  • One participant questions how a point, which has no dimension, can create a line that has dimension, expressing confusion about this relationship.
  • Another participant suggests that the issue is philosophical in nature and proposes redefining a point as an infinitesimal to address the confusion.
  • A participant acknowledges their ongoing confusion despite searching for answers and expresses curiosity about integrals in relation to the topic.
  • There is a suggestion to explore Zeno's paradoxes as they relate to the questions being raised, indicating that these inquiries have historical roots.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of the relationship between points and lines, and multiple competing views regarding the philosophical implications and mathematical definitions remain present.

Contextual Notes

Limitations include the philosophical nature of the discussion and the potential need for redefinitions, such as considering points as infinitesimals, which may not be universally accepted or applicable in all mathematical contexts.

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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