Infinity of infinities.

I can't help but wonder about the powers of human reasoning, limits that seem to be present on it and most of all by our inability to understand the very process.

When I was in school, the teacher taught us numbers from 1 to 10. We went from 20 to 50 and then to 100. I thought all the numbers have ended. All i needed to know about numbers was known! I could count, recite the whole list, write them. How happy I was and how wrong.

Addition caused a lot of problems, there were two carry overs in 87 + 34, too much trouble. The possibility of numbers with large number of digits seemed absurd. After all who would bother keeping track of them when the teacher asked you to add two of them.

Subtraction in class two, thankfully could be performed only from a larger number. Unfortunately numbers could be added and added, a whole new symbol of infinity appeared. I was perplexed. Why do we talk of numbers we cannot express. People have gone crazy. Then there was negative infinity and the square root of negative one - things that valiantly fought and held fort against my 'heroic' efforts to map them to real world objects.

Fractions were another set of troubles, adding them required you to have a common denominator. I wondered who came up with such complex rules. Mutiplying fractions was much easier, the product table could be put to good use here. In a next few years I learnt calculus, you can only approach a limit, but never reach it. An infinite number of points lay between you and the dreadful limit that the question paper asked. Only a leap of the mind to a theorem that summed the infinite set could make the professor happy.

All these years I have wondered, why we built infinity on infinity sought out to explain very abstract things as numbers. After all numbers don't have any connection to the physical world unless your mind makes one. Yet we struggle to understand the infinity of natural numbers, the infinity of reals that lay in between them and the same amount of numbers stretching away with the elusive i as a companion.

We have discovered rules to generate a number from the previous, one in between two others at all times. Yet every number is special, there is inly one pi and that occurs between the symbols 2 and 3 in our regular notation. Only a few sets simple restrictions like the pythogaras theorem. Some there are an infinite, some there are a few.

I still wonder, whether I an still the class 1 student who thought all mathematics was over when he could count upto hundred.