The concept of infinity can be hard to grasp. How can one understand something without end, something whish is forever and everywhere? How odd, then, that is actually is possible to work with infinity. It is not especially compliant, and often easy to lose track of, but some mathematicians have managed to wrestle it to the ground and keep it pinned long enough to get a prety good look at it. What they have found takes a good deal of explaination and a little bit of faith. Remember, the only thing infinity works like is infinity. And so, without further ado, let us begin at the beginning.
So, what exactly is infinity, anyway?
As this is not an easy question to answer, let us begin with a few things which infinity is not.
What Infinity Isn't
Infinity is not...
- Really, really big
- The farthest anyone can go
- In the set of 'real numbers'
- In the set of 'imaginary numbers'
- Normal in any way
Which brings us to...
What Infinity Is
So what is it then? Well, there is, as you have probably figured out by now, no clear or complete way to define it. It is cheifly itself. Conceptually, it is beyond any number at all. It is both greater and lesser than any number. Algebraically, it is the reciprocol of zero, that is, 1/0. In fact, infinity is any number over zero, and any value considered 'undefined' is most likely infinite. Perhaps the best way to define infinity is to understand it, and the best way to understand it is to work with it. That said, let us continue.