Wikipedia says that because of the limit of a/b as b approaches 0, a/0 can be defined to be a positive or negative infinite number, depending on whether a is positive or negative. There are a few more problems with this that Wikipedia didn't cover:

a/0 is neither positive nor negative
Now really, if you divide something by zero, which is neither negative nor positive, can it still be considered to be either? It certainly doesn't work like that when you multiply by 0. If you divide a positive number by a positive number, it's postive. If you do it by a negative number, it's negative. If you divide it by 0, it's... ?

a/b has two different limits depending on whether b is approaching from the positive or negative numbers.
If b is approaching from below, the limit of a/b is negative infinity. If approaching from above, it's positive infinity. Considering this, that number must be in between positive and negative infinity. What number is greater than positive infinity, but less than negative infinity? It's certainly not infinite.

0 times an infinite number is still 0
No matter how many times you add 0 to itself, it's still 0. Saying that an infinite number is the reciprocal of 0 implies that 0 times that number is 1.



That's about all right now. Questions? Comments? Logical errors? Reply! I might decide to add this to Wikipedia later.
(btw, myscrnnm, you're wrong)

n/0 has to be undefined because unless n is 0(in which case, any number would work) you can subtract 0 an infinite amount of times yet not get any closer. So therefore, division by 0 is impossible. I'd also like to see someone do n/infinity

According to my math book:
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/0 = Infinity

But,
0/5 = 0
0/4 = 0
0/3 = 0
0/2 = 0
0/1 = 0
0/0 = Any value at all, but it is not a defined value, so undefined.

but if you take 1/0 zero, and you subtract 0 an infinite amount of times, do you get 0? I thought that it was infinity in 6th grade, but after I actually thought about it, It is definitely undefined... and undefinable.

If you do it long enough, you'll get a definite answer, and it's one, but technically, if you do it forever you will get 0 somehow, I think.

One thing: using second order determinants, if you have D=0 and the Nx or Ny as 0, then you get the exact same line, which has a infinite amount of points that intersect. This is called a dependent graph. If you have the D = 0, but the Nx or Ny equal to something, then it doesn't have any points that interesect, which equals to zero. This is called a "inconsistient" graph.

Your math book sucks.


But the lines would be vertical, right? They'd have no real slope.

And if you stop time, then walk somewhere, you'd have a speed of 1/0. Then, you'd bump into things which would fly off at a speed of 1/0 also. And then the universe breaks.

Read: http://en.wikipedia.org/wiki/Determinant

Determinants are in this form:
ax+by=c
dx+ey=f
D = ae - db
Nx = ce - fb
Ny = af - dc

x = Nx / D
y = Ny / D

And by Nx and Ny, the x and y is in a subscript, since it means numerator(y)

I'm in intermediate algebra too. And... wait... no... i'm confused. Ohk. Now I get it. Right.

Although I accept the fact that x/0 is undefined (where x does not equal 0), some may argue that x/0 equals 0. I mean, when you divide a number into zero parts (which is basically what is happening when you divide by a number, you are turning it into that many parts), there will be nothing left, therefore the answer would be zero.

Heh, did you notice the fine print in the first post?


Also, for these reasons, x/0 cannot be 0:
☺How do you divide something into 0 pieces, and end up with the same amount of stuff that you had before? Because when you divide something into pieces, you always end up with the same amount of that thing, no matter how many times you cut it.
☺If x/0 = 0 when x isn't 0, we would get x=x when we multiply both sides of the equation by 0, right? But we don't. We get x=0.
☺How many times does 0 go into 1?

Also, 0/0 is undefined too. What times 0 equals 0? Any real number.

Lets look at the bottom line of n/0.
Lets take 1, for example. Lets do 1/0
1/0=undefined, or, according to lappy, infinity.
Lets use lappy's way, and make it infinity. Now lets check our work:
infinity x 0 = 0
Ooh! If it was correct, then it would be equal to 1, but it isn't, so, therefore, n/0!=infinity.

This makes me doubt your book meets standards...