Division by Zero - Can it be Done?

Click For Summary

Discussion Overview

The discussion revolves around the concept of division by zero, exploring whether it is possible to create a new number system that accommodates such operations. Participants consider various mathematical frameworks and implications of defining division by zero, including generalized complex numbers and alternative arithmetic rules.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the conventional avoidance of division by zero and propose the idea of a new number system that could incorporate it.
  • One participant mentions that division by zero can be approached through the concept of generalized imaginary numbers, suggesting that symbolic calculations might be possible.
  • Another participant argues that defining 0/0 leads to contradictions and that any structure allowing such definitions is either trivial or not a field.
  • There are discussions about specific examples where division by zero could be framed within limits or functions, but these do not resolve the fundamental issues raised.
  • Some participants express skepticism about the validity of operations involving zero, suggesting that they lead to illogical results.
  • Several participants engage in a debate about the implications of defining new rules for arithmetic involving zero, with some arguing that such rules could lead to inconsistencies.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the possibility of defining division by zero or creating a new number system. Multiple competing views and interpretations remain throughout the discussion.

Contextual Notes

Participants highlight limitations in their proposed systems, including contradictions arising from standard arithmetic laws and the implications of defining operations involving zero.

  • #31
If I said it, then quote it, don't make it up.
 
Mathematics news on Phys.org
  • #32
It's not even right to cancel functions where they are defined, let alone where they are undefined.

e.g. arctan(tan(180)) = 0
 
  • #33
negative factorials and division by zero

has anyone any thoughts on approaching division by zero through negative factorials? ie if you juggle the general definition of factorials you can arrive at 1/0 = (-1)! which is the rather interesting infinity -1 x -2 x -3 x...etc
How would this fit into the Cantorian hierarchy of infinities?
It has the property that it is neither negative or positive (or both), the sign changing with each subsequent term, which maybe (?) relates to the tan 90 thing, where the negative and positive tans are impossibly equal when 1/0 is introduced.
Anyway my brain is spinning already, someone put me out of my paradoxical misery quick!:confused:
 
  • #34
JonF said:
Futob:

Since you say that 1/0 = infinity

So is: 1/0 = 3/0

what about 1/0 – 1/0 = 3/0 – 1/0 is that equal?

Is 0/0 = 2/0?

I too would like some explanation about these statements.:bugeye:
 
  • #35
Since x/0 =inf ,where x is any number then 0*inf should be x.But 0 multiplied by anything is 0.And inf multiplied is inf. Someone please resolve this paradox.
 
  • #36
What paradox? Every 'paradox' is based upon making some false assumption and then getting a contradiction. This is no different. Your false assumption is that things ought to behave in some way when they don't.
 
  • #37
Vernon said:
How would this fit into the Cantorian hierarchy of infinities?

The infinity sign that appears in such things like this, singularities, is nothing to do with cardinals.
 
  • #38
matt grime said:
What paradox? Every 'paradox' is based upon making some false assumption and then getting a contradiction.
So the term "false paradox" is a pleonasm?
 
  • #39
I should have said 'every mathematical paradox'.
 

Similar threads

Undergrad Is a Vertical Line the Correct Depiction for this Equation?
  • · Replies 13 ·
Replies
13
Views
3K
High School What Are the Key Divisibility Rules You Need to Know in Mathematics?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Where has this proof gone wrong? ∞= 1/0
  • · Replies 36 ·
2
Replies
36
Views
5K
Undergrad Is the division of zero by zero a true division?
  • · Replies 7 ·
Replies
7
Views
3K
MHB Prove a number is divisible by a number?
  • · Replies 7 ·
Replies
7
Views
2K
High School Math contest division question
  • · Replies 3 ·
Replies
3
Views
1K
High School A proper comprehensive rule for arithmetic operation precendence
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Why dividing zero by zero remains a problem
  • · Replies 28 ·
Replies
28
Views
5K
High School Creating Log Tables: Briggs' 400-Year-Old Accomplishment
  • · Replies 10 ·
Replies
10
Views
3K
High School Problems Understanding Division of Fractions
  • · Replies 2 ·
Replies
2
Views
2K