Wust Jondering...

"undefined" is a placeholder for the solution that is not defined

Think of it like a multivalued operation.
[eqn]0\cdot a=0~\forall a\in \mathbb{C}[/eqn]

what number multiplied by zero gives you the original number?

15/3 = 5

3*5 = 15

15/0 = undefined; because

0 * ?? = 15

see. fill that ?? in with a number and you get a fields medal AND i will suck your dick

>>8578824
>How can one divided by zero equal undefined, if it's been defined as being undefined? Isn't that a self-contradiction?
the reason is that zero is the neutral element of addition and this necessarily makes zero have no multiplicative inverse:

if a + 0 = a then

a*0 = a*(0+0) = a*0 + a*0
-> a*0 = 0. for any a. (*)

BUT for an inverse of an element a you have the equation
a*a^-1 = 1.

if you now chose a = 0 you get
0 * 0^-1 = 1 which contradicts (*)

Therefore zero does not have a multiplicative inverse.

>>8578845
>Using the language of abstract algebra to someone who does't understand division by zero

======^]]]]]]]]

>>8578839
0 * -15/12 = 15

;^)

>>8578847
>multiplicative inverse

yeah dude, better watch out or he just might start lecturing OP on galois theory haha!

>>8578824
it's because 0 is not a real number

A wheel is the name for that kind of algebraic structure, but it's not very interesting.

>>8578824
>How can one divided by zero equal undefined

Because your calculator is programmed that way.

>>8578824
>>8578839
You can divide a pie for 1 person, two persons, n people.
Can you divide a pie for 0 people ? No, you can't.

>>8580317
can you devide a pie by -1 person?

>>8580321
Sure you can. Write an IOU for some fraction of a pie.

>>8578824
You all are retarded. Math is symbol manipulation. Undefined means that for the symbol sequence 1/0 there is nothing you can replace it with defined by the system without fucking up everything. For example 1+1 you can replace with 2 and so on. The symbols don't mean anything.