1/infinity leads to undefined operation

1/infinity is the quantity that when multiplied by infinity gives 1, which is 1/infinity.

But we can show that it is an indeterminate value that leads to this result, while still technically making it a true result. Because (1/infinity)*infinity=infinity/infinity which is indeterminate as it equals any positive value, which includes 1. But it also equals 2 or any other positive real.

This shows that 1/infinity can equal 2/infinity or n/infinity for any positive real n.

1/infinity=0 In fact, any real n/infinity is equal to zero. Because this has been shown to be true, 1/infinity is not an indeterminate. However, (1/infinity)*infinity is an indeterminate, since 0*infinity is an indeterminate form. To put it in a way that the non-math nerd reader can understand, as the number you divide by increases, the number gets smaller and smaller. Here is an example. 1/10=0.1 1/100=0.01 1/1000=0.001 1/1000000=0.000001 Eventually, the decimal is so small that it is considered to be zero.

You're ignoring my post that demonstrates standard rules of operation in mathematics.

If a/b equals a/b then (a/b)*b=a/b as a/b is the number or ratio that must be multiplied by b to reach a.

Like wise, 1/infinity is the number that when multiplied by infinity equals 1. So that (1/infinity)*infinity=infinity/infinity does technically equal 1, but equals any positive real as well.

But the point was that when dividing 1 by infinity the indeterminate fraction of infinity/infinity is reached.

I'm not sure why you posted that message and what it is supposed to prove?

Infinity is not technically a number, so the standard rules of operation do not apply to it. If you want to get technical, infinity is really a direction that can be approached, but never achieved. 

To expand on my example in post #3, 1/some power of ten (10^n) will give a decimal that has n-1 zeros in front of a one. Eventually, as the n approaches infinity, the number of zeros in the decimal will also approach infinity. This makes the decimal so infinitely small that it is said to equal zero. I used this example to demonstrate that (1/infinity)*infinity is an indeterminate, since 0*infinity is an indeterminate. It is considered an indeterminate because it can return different values in different functions. In order to find the value it produces, the function must be manipulated to the form 0/0 or infinity/infinity. Once it achieves this form, L'Hopital's Rule can be applied to determine the value of 0/infinity in that specific case.