Understanding 0/0: Infinity, 0, and 1

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Discussion Overview

The discussion centers around the mathematical expression 0/0, exploring its implications in mathematics and physics. Participants examine the nature of division by zero, particularly in the context of physics equations involving mass and speed, and the concept of singularities.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants assert that division by zero leads to infinity, while others argue that division by zero is undefined.
  • A participant references a physics equation involving mass and speed, questioning the outcome when substituting values that lead to 0/0.
  • Another participant clarifies that the equation discussed is only valid for massive particles, suggesting that one should not attempt to divide zero by zero.
  • There are mentions of different types of singularities that can arise in mathematical functions, indicating the complexity of the situation when approaching 0/0.
  • One participant acknowledges a correction regarding the nature of a singularity in a mathematical expression.
  • A participant emphasizes that 0/0 is fundamentally undefined.

Areas of Agreement / Disagreement

Participants express disagreement regarding the nature of 0/0, with some asserting it leads to infinity and others maintaining it is undefined. The discussion remains unresolved with multiple competing views on the topic.

Contextual Notes

Participants note that certain equations are only applicable under specific conditions, such as the mass of particles being non-zero. There is also mention of removable and essential singularities, which adds complexity to the understanding of 0/0.

madmike159
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What is 0/0.
Any thing devided by 0 is infinity, 0 devided by something is 0 and anything devided by itself is 1.
 
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madmike159 said:
What is 0/0.
Any thing devided by 0 is infinity, 0 devided by something is 0 and anything devided by itself is 1.

No, division by zero is undefined. If you want this thread to accomplish anything then you should do it soon before a moderator closes it.
 


I started thinking aabout it when I was looking at a physics equation.

m = m0/sqrt(1-v^2/c^2)
*sorry the equation options arn't working for me*

If a particle with no mass like a photon which moves at the speed of light then its mass at rest (0) is devided by 1 - c^2/c^2 = 0. I just wondered what 0/0 was, I know that this equation has no real proof.
 


The equation is only valid for massive particles, and they move slower than the speed of light, so you never attempt to 'divide zero by zero'.

There are many occasions where, if on substituted values of variables in, one would end up with 0/0. This really means you just need to be careful. There may be a removable singularity (eg sin(x)/x at x=0), a singularity like 1/x or 1/x^x at 0, or an essential singularity (such as log(z) at 0), when viewed as a function from C to the extended complex plane. The nature of the singularity may tell you something useful.
 


matt grime said:
The equation is only valid for massive particles, and they move slower than the speed of light, so you never attempt to 'divide zero by zero'.

yea I know, it just made me think about it.
 


I meant to write 1/x^2, not 1/x^x, which is almost surely an essential singularity.
 


0/0 is truly undefined in its nature.
 

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