Given previous arguments in the division by zero matter, I have opted to move this argument into this thread where it properly belongs...

If division by zero produces a result of infinity, then
(1/0) = infinity.
If we multiply both sides by 6, we get
0 = infinity * 1

By the same assumption, (100/0) = infinity as well.
Therefore, 0 = infinity * 100

Since both expressions are equal to zero,
infinity * 1 = infinity * 100

And cancelling the infinities, we are left with.
1=100.

This proves that division by zero does not produce infinity, if we accept that 1 does not equal 100.
If we assume that division by zero is infinity, then we must also assume that one equals one hundred. I wish you were writing my paychecks, nihil.

It can be philosophically argued whether or not infinity actually exists, and mathematically one can argue either way.

But if we let a equal infinity, then what does 1/a equal?

Let us assume that infinity + 1 = infinity.

Therefore, a + 1 = a
Now divide all terms by infinity:
(a/a) + (1/a) = (a/a)
And let (1/a) = b, so that:
(a/a) + b = (a/a)
Therefore, subtracting (a/a) from both sides,
b = 0
Or, (1/infinity) = zero.

We have now proven that (1/infinity) equals zero. If we divide one by ten, the result is 0.1. If we then multiply by ten, the result is again 1.

However, if we divide 1 by infinity, the result is zero, and anything multiplied by zero is zero. This is not a disputed fact. Division by zero is.

So,
(1/infinity) * infinity = 0
If we cancel the infinities, we are left with

1=0

And everything we know is wrong.

Abtronic, the problem in the following solution is the cancelling of (a-b) where a and b are equal. This is division by zero. This was an example used to teach me the consequences of division by zero.

a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
(a + b) = b
1 + 1 = 1
therefore 1 = 2.

The point: The concept of infinity is beyond the realm of human comprehension. We therefore cannot express it as an answer.

Any solutions to this paradox?