According to prominent mathematicians, if you divide zero by zero you get the set of real numbers. A mathematician set me that precise problem and I got the set of real numbers by a slightly dodgy method. He confirmed to me that I had the correct answer, and also confirmed to me my suspicions that my method was not rigorous enought. He then told me a rigrorous method:
Plot a/b on the y-axis versus b on the x axis where a is (presently) a constant.
You get a hyperbola.
Now, limit both a and b to zero.
the hyperbola approaches the axes as you do so, until you are left with a number line from which you can select any real number.