Quote:
Originally Posted by oldsilver
The intention was to query whether 1/0 might be some entire universal set larger than any +/- linear infinity, as 1/0 seems to be intuitively non linear. But I might just be puffin muffins there and will check those videos.
You should think for a moment about what you mean when you say the symbol "1/0" represents a "set."
When you think about a number like 6, is that also a "set"? What do you think a "set" is?
There is value to thinking about 1/0 as a limit. You can get interesting properties out of it that way. But it's not a "number" in the algebraic sense (PTB showed how it fails some basic algebraic properties).
I really think you will want to be looking back at the topological properties. Start with the two point compactification (infinity and -infinity are two different points on opposite ends of the real line), and then imagine bringing those two distinct values together and creating a circle. Now you have just one point serving as infinity, and you have a way of transporting yourself across an "infinite" distance.
There's something interesting there, but it's not really happening the way you're thinking about it. You need to hone in that language a little bit more and get clear on what your underlying picture is.
(If you want to go beyond the traditional infinity, you might want to try transfinite numbers. But I don't think you can get there from thinking about 1/0.)