Hi Andrew,
That quite a story, but I’m afraid I can’t follow your line of reasoning and arguments.
To me, the bottom line is that zero AND infinity are both self references and therefor will always give problems in math. You simply cannot use them in a reliable way, they are error prone. They are not numbers but concepts, it is nonsense to add zero to some number, subtract it from some number, multiply some number with it or divide some number with it.
take:
34 * 0 = 0
and
12 * 0 = 0 (pick any number…)
this leads to 34 * 0 = 12 * 0
the zero’s cancel out and so we have the statement 34 = 12 (or any number…)
Nonsense! And only because zero is a reference, not a number. Have you seen zero sheep? Zero green aliens? Zero stolen Picasso’s? Well come to my house, I have them all, next to zero Cadillac's and zero guitars that Jimi Hendrix played (quite fond of them actually…). Nonsense!
In set theory, there’s the empty set, right? Nonsense! It contains nothing so it’s a self reference and does not qualify as a valid set!
Draw any diagram, any grid on any sheet of paper, use the center as reference and call it zero. And you can use it to maken calculations and draw graphs. You don’t need actual coordinates in space to be able to do that, you only need to pin zero somewhere, draw a grid and you’re good to go. It’s a reference!
Likewise with infinity, it is a concept that — and that is a very important notion overlooked by math-magicians — involves TIME.
If you keep repeating something over and over again for infinity, you can safely speak of an infinite value. But at the very moment you stop, you get stuck with a finite number, whatever the size may be. No single value is instant infinite, freeze whatever moment in the history of the universe and you end up with concrete values, finite and precise. Infinity means it goes on and on and on. How do you ever get to an infinite….something (take space for example)? By letting space expand… for infinity. How do you reach a infinite amount of something? Just keep making more of it…for eternity. Stop and you are left with a finite number. Simple as that!
Infinity was only conceived as an answer to what do you get when you divide something by zero? But the question was wrong in the first place! You can not divide by zero for it is a concept, not an actual number. Plus it is self referential, because it references nothing else but itself.
If infinity pops up in some math equation… you’re just doing something wrong. And in most of the times it involves zero’s and/or self references (and thus creating infinite loops). So be careful with what you try to calculate if it involves zero’s and infinities, because math is incomplete, not concise and flawed as a language.
Have a nice day!
Mark
