Infinity again

[wendy]

Infinity, like dividing by zero, sometimes works.

It's like if you have a large crowd of people. You ask a question to X, and sometimes X answers, and sometimes Y answers. If you can rely on X answering, than 0/0 is the same as X/X, is quite definite.

Sometimes, you can tell that Y and X are related by a common mantissa or modulus, and therefore you can use some information, but not exactly.

Sometimes, you can replace an infinite sum that goes nowhere by another property that goes somewhere.

Infinity does not just "happen", but has an "onset" of loss of information.

Split from "Forum inactivity" ~Keiji

[Keiji]

I consider zero to be the absense of anything, and infinity to be the presence of everything, rather than considering them as numbers.

If you use the number circle rather than the number line for real numbers, then it makes more sense to use a sphere rather than a torus for the complex numbers. By using the sphere, zero is at the bottom, infinity is at the top (just like the number circle), the distance "up" the sphere's surface is <i>r</i> and the angle around the sphere horizontally is <i>θ</i>. This is like taking the complex plane and squashing it into a sphere with the origin at the bottom.

Obviously, on the number sphere, there is no such thing as a "directed infinity" (ie. a number with infinite <i>r</i> but defined <i>θ</i>). To me, a directed infinity makes just as little sense as a directed zero.