Infinity is that number which is always slightly bigger than the largest number you can imagine¹. Sounds frustrating? Well it really is...

For many years people were annoyed to find that while they tried to count as high as is humanly (or insert-name-of-race-here-ly) possible, they never actually reached a point that they could call a convenient stopping point. Instead they invariably grew bored, and went off for a nice cup of tea, or perhaps a long soak in a bath. Then one day a bunch of friendly mathematicians sat down and had a good think about the problem. They scratched their heads for a while, and soon the ideas were flowing from their collective brains, much as water can be seen to flow from a rock. They debated² the possibility of choosing one number (say 42) and defining this as the largest possible number. This would mean that you could not count higher than 42. Ever. This has certain obvious advantages (you can never truly feel old for instance) but several equally obvious disadvantages (you could, for instance, never own more than 42 Altarian dollars). Fortunately, one wise guy raised the issue of 43.

After many wasted tea bags (or well utilised tea bags - this largely depends on your beverage preferences) someone else had an idea. A brilliant idea. It would be nice to attribute the concept of infinity to someone, that way all the blame could be laid on them (for prosperity’s sake you understand, not to make a scapegoat of someone who is probably dead by now). Unfortunately, it was an anonymous suggestion posted to an anonymous suggestion box. The suggestion was very simple, so simple that a layman (or woman, vogon, or in fact any other race) could understand it. The idea was this:

We cannot count to the highest number simply because the highest number does not exist. You can never reach it; it is in fact not a number, merely a concept. (The actual suggestion slip said "Can I have some toast please?" but after considerable translation the currently accepted conclusion was reached).

This concept seemed to be a brilliant idea! An ideal solution in fact. Why try to find the biggest number when you can just give a name to it and ignore it in the hope that it will go away. This method can be seen to work with siblings and bullies, so no one saw any reason for it not to work with a mathematical theory.

Trying to understand infinity

To try and wrap your head(s) around the concept of infinity is a tricky problem, and there are several suggested methods, although no one has actually succeeded. The risks involved are so great that we cannot even begin to contemplate describing the methods here; but if you're interested, have a Pan Galactic Gargle Blaster and then walk into a brick wall. You'll begin to get an idea of infinity.

Infinite Sums

Addition: Interesting things happen when you try to perform normal mathematic functions with infinity. While it is generally accepted that 2 + 3 = 5, it’s harder to accept that infinity + 3 = infinity. What about infinity + infinity then? Well, strangely enough this also equals infinity.

Subtraction: 5 – 3 = 2. Obviously. What about infinity – 3 then? Well, it equals infinity. How can this be though? Surely if you take something away from something, then the first something will become smaller? This is logical. Infinite sums are however much easier than normal sums; to perform them requires no knowledge of maths, and no application of logic. Infinity – infinity? There’s a tricky one…

Multiplication: 2 * 3 = 6. Infinity * 3 = infinity³. Beginning to understand the pattern here? I hope so. Perhaps you could work out Infinity * 2 for me…. What about infinity * infinity then? Well, yet again, this equals infinity.

Division: 6 / 3 = 2. Infinity / 2 = infinity. This should become apparent upon examination of the problem. How many times does 2 go into infinity? It goes in an infinite time of course!

Powers: 2 ^ 3 = 8 (2 * 2 * 2 = 8). Infinity ^ 2 = infinity (infinity * infinity = infinity). How about infinity ^ infinity then? Well, this is also infinity, but it’s a different type of infinity!