Simple Proof That Division By Zero Is Impossible

  • Thread starter Poolala
  • Start date
  • #1
2
0

Main Question or Discussion Point

x / y = z, so z * y = x
1 / 0 = x, so x * 0 = 1
But 0 does not equal 1, so x / 0 is unsolvable.
Oh, and I'm new to forums so if this shouldn't be here you can delete it.
 

Answers and Replies

  • #2
95
2
Perhaps you want to look at:

[itex]\underbrace{lim}_{i->0} \frac{Sin(x)}{x} = 1[/itex]
 
  • #3
Simon Bridge
Science Advisor
Homework Helper
17,841
1,642
You mean:
$$\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1$$

... mathematicians can set up numbers to do all kinds of things.
 
  • #4
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
x / y = z, so z * y = x
1 / 0 = x, so x * 0 = 1
But 0 does not equal 1, so x / 0 is unsolvable.
Oh, and I'm new to forums so if this shouldn't be here you can delete it.
This argument makes the assumption that, whenever x/y is defined, the equation y(x/y) = x holds. It also makes the assumption that x0 is always defined, and it is 0.

Both of these assumptions are, indeed, true for the real number system, and the complex number system. But other important number systems do not have these properties.



RamaWolf is talking about something different (although some people have trouble distinguishing the two).
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,770
911
x / y = z, so z * y = x
1 / 0 = x, so x * 0 = 1
But 0 does not equal 1, so x / 0 is unsolvable.
Oh, and I'm new to forums so if this shouldn't be here you can delete it.
Yes, that's a perfectly valid proof that the number 0 (or the additive identity in any field with more than one member) does not have an inverse.

Perhaps you want to look at:

[itex]\underbrace{lim}_{i->0} \frac{Sin(x)}{x} = 1[/itex]
True but has nothing to do with the topic here.
 
  • #6
2
0
Oh, and I've been thinking: does 0 / 0 = 1, or is it undefined?
 
  • #7
841
0
Oh, and I've been thinking: does 0 / 0 = 1, or is it undefined?
In most number systems 0/0 is undefined. Only a few exotic number systems have defined it and that is outside my scope.
 

Related Threads for: Simple Proof That Division By Zero Is Impossible

  • Last Post
2
Replies
39
Views
12K
  • Last Post
Replies
18
Views
12K
Replies
2
Views
2K
Replies
7
Views
9K
Replies
1
Views
424
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
12K
Top