Confusion about a point and a line

In summary, the conversation discusses the concept of dimension in mathematics and how a point, which has no dimension, can create a line, which has dimension. The idea of redefining a point as an infinitesimal is suggested as a way to understand this concept. The conversation also mentions the limitations of discussing philosophy on the topic of infinity and suggests research on Xenos paradoxes.
  • #1
anhnha
181
1
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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  • #2
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.
 
  • #3
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?
 
  • #4
Is there an direct explanation to this even philosophy?
See the link. Also research Xenos paradoxes.
The questions are that old.
 

1. What is the difference between a point and a line?

A point is a location in space with no length, width, or depth, and it is represented by a dot. A line, on the other hand, is a set of points that extend infinitely in both directions and has length but no width or depth.

2. Can a point be considered a line?

No, a point cannot be considered a line because it does not have length or direction, which are essential characteristics of a line.

3. How do you determine if a point lies on a line?

To determine if a point lies on a line, you can use the slope-intercept form of a line equation (y = mx + b). Plug in the coordinates of the point for x and y, and if the equation is true, then the point lies on the line.

4. Is a line segment the same as a line?

No, a line segment is a portion of a line with two endpoints, while a line extends infinitely in both directions without endpoints.

5. Can a line and a point be parallel?

No, a line and a point cannot be parallel because a point has no length or direction, so it cannot be compared to a line in terms of parallelism.

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