Divide By Zero: Is It Ever Logical Not To?

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Discussion Overview

The discussion revolves around the concept of division by zero, exploring whether there are logical scenarios in which it could be considered valid or meaningful. Participants examine the implications of dividing by zero in mathematical contexts, including theoretical and conceptual considerations.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that division by zero is inherently illogical, while others question whether it could yield a meaningful result, such as zero or infinity.
  • One participant proposes that dividing a non-zero number by a very small number approaches infinity, suggesting a potential interpretation of division by zero as infinite.
  • Another participant argues that if division by zero were defined, it would lead to contradictions, such as 0=1, which indicates a fundamental problem with such an operation.
  • Some participants discuss the ambiguity of dividing by zero, noting that it can lead to undefined or indeterminate forms, particularly in the context of limits and infinity.
  • There are mentions of mathematical constructs, such as projective planes, where division by zero might be permissible but leads to complications.
  • Several participants express that treating infinity as a number in arithmetic operations can lead to nonsensical results, emphasizing the need for caution in such manipulations.
  • One participant highlights that while some operations involving infinity can be useful in limits, they should not be treated as standard arithmetic.
  • Discussion includes the idea that certain notations, such as limits approaching infinity, may be misleading but are accepted in mathematical practice.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus on the validity of dividing by zero, with multiple competing views presented. There is significant disagreement regarding whether division by zero can yield meaningful results or if it is fundamentally flawed.

Contextual Notes

Participants express various assumptions about the nature of infinity and division, with some relying on specific mathematical frameworks that may not be universally applicable. The discussion also touches on the limitations of conventional arithmetic when dealing with infinity.

  • #31
then the line would have no slope because change in y would also be zero

Edit: read next post
 
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  • #32
gregmead said:
then the line would have no slope because change in y would also be zero

That is exatly my point. \frac {y_1} {x_1} Or \frac {y_2} {x_2} have to result in 0, and then after you add the interception point of y you can get your straight line. :smile:
 
  • #33
Edit: sorry misunderstood

if dx=0 then the slope WILL be infinite, eg undefined, not equal to 0. It will be vertical, which when you think about what slope means and what the graph is telling you, makes sence.
 
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  • #34
Since when is slope \frac{y_1}{x_1}-\frac{y_2}{x_2}? Isn't it \frac{y_1-y_2}{x_1-x_2}?

In that case, if the two x values are the same, then the slope is vertical. Vertical slope is orthogonal to zero slope, so you can hardly say that division by zero results in zero.
 
  • #35
Moo Of Doom said:
Since when is slope \frac{y_1}{x_1}-\frac{y_2}{x_2}? Isn't it \frac{y_1-y_2}{x_1-x_2}?

In that case, if the two x values are the same, then the slope is vertical. Vertical slope is orthogonal to zero slope, so you can hardly say that division by zero results in zero.

you have a point there, but if the two x values are the same then what exactly are we trying to prove? that the graph will tend to infinity in the y direction as the function approaches the limit where the gradient is \frac{1}{0}, ie undefined, ie a number much greater than we can work with, ie the gradient is mahoosive, ie vertical?

which has been shown on oh so many graphs over the years, for example the classical y=\frac{1}{x}, where at the point x=0, the function is undefined and has an asymptote

it is worth pointing out gregmead's point on the fact that \frac{1}{0} is undefined as opposed to "infinity". "infinity" is actually a bungled job on the part of physicists, because they like to say (for example) bring a charge in from infinity... well, that raises the question "what does that mean?"
 
  • #36
The error is in the zero

The sorry is a absolute zero being true.
In math, it is right.
In nature, it is ease to division but in math or phys is not right.
The sorry as God in another world. :smile:
 

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