What is the Fraction of One Point Compared to an Infinite Line?

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In summary: However, this is not commonly used in elementary mathematics.In summary, the fraction of a single point compared to a line is 0, as the "length" of a point is 0. Division by infinity is not allowed and is considered meaningless. The area of contact between a perfectly round object and a flat surface depends on the definition of the object, but for a disk it is the area of the disk and for a sphere it is 0. Division by infinity can be made rigorous through complex infinity on the Riemann sphere, but it is not commonly used in elementary mathematics.
  • #1
CrossboneSRB
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So here's a question for you, if on a line we chose one point, then what is the fraction of this point compared to the line?
I think we all agree that between two points there are infinite amount of other points, correct? So what fraction of a line is one point among infinite others? Isn't it 1/∞?

Here's another question, if a perfectly round object is placed on perfectly flat surface, what is the area of contact?
 
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  • #2
CrossboneSRB said:
So here's a question for you, if on a line we chose one point, then what is the fraction of this point compared to the line?
0. The "length" of a single point is 0.
CrossboneSRB said:
I think we all agree that between two points there are infinite amount of other points, correct? So what fraction of a line is one point among infinite others? Isn't it 1/∞?
No, because we don't calculate length on the basis of how many points are in an interval. We calculate length by subtracting the position of the point on the left from the position of the point on the right. The length of an interval [a, b] between two points (assuming a < b) is b - a.

The ratio of the "length" of a point to the length of the line segment [a, b] is 0/(b - a) = 0.

In any case, division by ∞ is not allowed.
CrossboneSRB said:
Here's another question, if a perfectly round object is placed on perfectly flat surface, what is the area of contact?
Your question isn't very precise. A circular disk is a perfectly round object, so the area of contact would be the area of the disk.

If by "perfectly round object" you mean a sphere, there is only one point of contact, so the area of contact would be zero for reasons similar to what I already gave.
 
  • #3
Infinity cannot be treated as a normal integer or real number. It is not part of one of these sets of numbers. In that sense 1/ꝏ is meaningless.

You can use the infinity concept in limits. Going to infinity means taken larger and larger values (ꝏ is not a number that can ever reach)

The limit of 1/x as x approaches Infinity is: 0For the second question: when a plane "touches" a sphere they have one point in common. The area of contact is therefore 0
 
  • #4
The concept of division by infinity can also be made rigorous, instead of using limits, by considering complex infinity on the Riemann sphere.
 
  • #5
Is it a point, a line, or a fraction of the object's area?

The fraction of one point compared to an infinite line is a concept that can be interpreted in different ways. From a mathematical perspective, the fraction would be considered as 0, since a point has no measurable length and therefore cannot be divided into smaller parts. However, from a physical perspective, we can think of the fraction as being infinitely small, approaching 0 but never actually reaching it.

In the context of your question, the fraction of one point compared to an infinite line would depend on the specific point and line in question. If we are considering a specific point on a line, then the fraction would be 1/infinity, as you mentioned. However, if we are looking at the entire line as a whole, then the fraction would be 0, as the line contains an infinite number of points.

Regarding the question about a round object on a flat surface, the area of contact would also depend on the specific object and surface. If we are looking at a perfectly round object on a perfectly flat surface, then the area of contact would be 0, as a point has no area. However, if we are considering a slightly imperfect object or surface, then the area of contact would be a fraction of the object's area. Again, this highlights the idea of approaching but never reaching 0 or 1/infinity.

Overall, the concept of fractions in relation to points and lines can be a bit abstract and can vary depending on the context. It is important to consider both mathematical and physical perspectives when discussing such concepts.
 

1. What exactly is the concept of "1/∞ discussion maybe"?

The concept of "1/∞ discussion maybe" is a theoretical discussion about the idea of infinity and the possibility of breaking it down into smaller, finite parts. It explores the idea that even though infinity is technically unattainable, it can still be approached or divided into smaller units.

2. How is this concept relevant in the field of science?

This concept is relevant in the field of science as it challenges our understanding of infinity and its implications in various scientific theories and concepts. It also encourages critical thinking and exploring new perspectives in the scientific community.

3. Who first introduced this concept and where can I learn more about it?

This concept was first introduced by philosopher and mathematician Georg Cantor in the late 19th century. There are many resources available to learn more about this concept, including books, articles, and online discussions among scientists and mathematicians.

4. What are the potential applications of understanding "1/∞ discussion maybe"?

Understanding this concept can have potential applications in various fields of science such as physics, mathematics, and cosmology. It can also lead to new breakthroughs and advancements in these fields by challenging traditional ways of thinking.

5. Are there any controversies or debates surrounding this concept?

Yes, there are ongoing debates and controversies surrounding this concept, as it challenges traditional beliefs and theories about infinity. Some scientists argue that it is purely a mathematical concept with no real-world applications, while others believe it can have significant implications in understanding the universe and its infinite nature.

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