What is the inverse of infinity in geometry?

Click For Summary

Discussion Overview

The discussion revolves around the concept of the "inverse of infinity" in geometry, exploring different interpretations and implications of this idea. Participants examine the notion of inversion in geometric contexts and the mathematical implications of dividing by zero.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant recalls a method suggesting that zero is the inverse of infinity and requests a reference for this claim.
  • Another participant questions the meaning of "inverse," introducing the concept of inversion in a circle, where points can be related through distances to a center point.
  • This participant emphasizes that there is no established proof that 1/0 equals infinity, asserting that infinity is not a number in conventional arithmetic and that division by zero is undefined.
  • A later reply draws an analogy, comparing the question of 1/0 to nonsensical queries about unrelated topics, suggesting that such questions lack meaningful answers.

Areas of Agreement / Disagreement

Participants express differing views on the concept of the inverse of infinity, with no consensus reached on the validity of zero as its inverse or the implications of dividing by zero.

Contextual Notes

Participants highlight limitations in the discussion, particularly regarding the definitions of "inverse" and the mathematical treatment of infinity and division by zero, which remain unresolved.

Pjpic
Messages
235
Reaction score
1
I seem to recall reading a geometry method that showed zero to be the inverse of infinity. Can you give me a reference for that?
 
Mathematics news on Phys.org
That depends upon what you mean. "Inverse" in what sense? You can, for example, use "inversion" in a circle. Given a circle of radius "R" and center "O" and a point P inside the circle, we define its "inverse" to be the point, Q, lying on the same extended radius of the circle as P, such that |OP||OQ|= R^2 where |OP| and |OQ| are the distances from O to the two points. If P is on the circle, Q= P. As we move P closer to the center of the circle, the corresponding Q moves farther and farther from the circle. As P approaches the center, in the limit, Q goes to infinity.

But if you are looking for a "proof", geometrical or otherwise, that, in our usual arithmetic 1/0 is equal to infinity, that just isn't going to happen. It simply isn't true. There is no number called "infinity" in our usual arithmetic and you cannot divide 1, or any other number, by 0. "Infinity" is just a "shorthand" for limits.
 
Asking what 1/0 is is like asking what the color of an electron is. Or, whether or not the king of France is bald!
 
ellipsis said:
Asking what 1/0 is is like asking what the color of an electron is. Or, whether or not the king of France is bald!
NO! I am not bald!
 

Similar threads

High School Are Inverse Problems More Complex Than Direct Problems in Mathematics?
  • · Replies 13 ·
Replies
13
Views
3K
High School Three Squares Problem
  • · Replies 10 ·
Replies
10
Views
2K
High School Rigid Transformations and other topics -- help with Learning Geometry?
  • · Replies 4 ·
Replies
4
Views
2K
High School Can a log have multiple bases?
  • · Replies 44 ·
2
Replies
44
Views
5K
High School Is Infinity a Prime Number: The Confusing Concept of Infinity Explained
  • · Replies 19 ·
Replies
19
Views
5K
High School Is Infinity x 0 Equal to Zero?
  • · Replies 5 ·
Replies
5
Views
8K
High School Inverse Functions vs Inverse Relations
  • · Replies 4 ·
Replies
4
Views
4K
High School How to find the inverse of this equation
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Ancient mathematics/History of mathematics
  • · Replies 11 ·
Replies
11
Views
3K
High School Is Infinity Cyclical or Linear?
  • · Replies 35 ·
2
Replies
35
Views
5K