Dividing by zero

[naimless]

Is zero even really a number?

[vorlon13]

It's not the absence of a number . . .

[Zidneya]

Ow, my brain...

Believe me Stimbo I know the feeling.

[Mudhammam]

I'm not a math wiz. Why is it you can multiply by zero and get zero but you can't divide by zero?

Why doesn't 1/0 equal 0 but 1*0 does? Is there a reason or is it arbitrary?

One minus one divided by one minus one.

Did it! :-)

[StealthySkeptic]

[Alex K]

Can't we simply say that dividing by zero is an abomination unto God, and leave it at that???

...damn, wrong forum.

One comment though (I hope noone made it yet):

What one can and cannot do is always a question of definitions.
One can for example extend the field of real numbers with "+" and "*" as operations by a quantity called infinity,

http://en.wikipedia.org/wiki/Alexandroff_extension

and then declare that by definition to be the value of x/0 (though what is 0/0 then...). The problem is that no matter how one defines x/0 in one's extension of the real numbers, one invariably loses cherished properties of the field of real numbers which one would like to preserve in order to do calculations with it - such as every number having a unique inverse with respect to "+" and "*".

So I'd rephrase the question slightly from

"why can't I divide by zero"

to

"Can't I consistently define the division by zero in some generalization of the field of real numbers without losing certain properties?".

The latter is a well-defined question which can be proven, and the answer is: no, you can't.

Taking limits is a concept invented in the 17th century. By now, it's really kindergarten stuff compared to complex integration and Residue theory.

Residue theory was invented in the 19th century. It's also kindergarten stuff compared to the things invented in the 20th century. Algebraic topology anyone?

[Mudhammam]

Alex K returns! Welcome back! :-)

[Alex K]

Alex K returns! Welcome back! :-)

Thanks, I appreciate it. Personal matters kept me away for a while...

Hmmm, why do I suddenly crave a nice cohiba?

[robvalue]

Here's a little trick I like to play on people, many of you have probably seen it before.

Given

a = b

Multiply both sides by a

a^2 = ab

Subtract b^2 from both sides

a^2 - b^2 = ab - b^2

Factorize both sides, LHS is difference of two squares.

(a+b)(a-b) = b(a-b)

Cancel out the (a-b) on both sides

(a+b) = b

But since a=b

b+b = b

2b = b

Cancel out the b on both sides

2 = 1

[StealthySkeptic]

Here's a little trick I like to play on people, many of you have probably seen it before.

Given

a = b

Multiply both sides by a

a^2 = ab

Subtract b^2 from both sides

a^2 - b^2 = ab - b^2

Factorize both sides, LHS is difference of two squares.

(a+b)(a-b) = b(a-b)

Cancel out the (a-b) on both sides

(a+b) = b

But since a=b

b+b = b

2b = b

Cancel out the b on both sides

2 = 1