Tuesday, August 29, 2006

Infinity Causes Infinite Confusion

For last 3-4 weeks I have been spending a hell lot of time on Orkut Mathematics community. And for last few days I have been finding a lot of posts on the topic of infinity. The confusion around the word infinity is so great that I was in total awe. Almost all the posts were way wrong about infinity. (I think most of the smart people who had no confusion probably did not bother to post.)

There was lot of discussion on things like 1/0 = inf, 1/inf = 0, inf/inf = 0, inf/inf = 1 and other confusing beasts. Most of the people participating in the discussion were mostly students of 11th and 12th grade from various countries. This is the time when most people meet infinity in their mathematics classes. (I also met it during the same period of my life, but more on that in some other post.)

The most common form of confusion was around 1/0 = inf. Most of the people argued that when we make the denominator smaller and smaller in 1/x, then the fraction gets larger and larger and when denominator x becomes equal to 0 then the fraction 1/x becomes equal to infinity. Now that's a highly absurd statement, but people involved are excusable because on their first date with infinity, almost everyone feels the same.

There were some posts by people were engineering graduates and I was surprised to find that they still had similar feelings about the beast. I don't think that is excusable because almost all engineering courses have some course in basic calculus. But anyway, the real culprits are the teachers, professors and worst of all, the book authors who fail to explain even the very basic concepts like infinity.

I really felt very sad about all this state and tried to help them in whatever way I could by posting a lot of stuff about infinity. I gave very simple example and explained in great detail. For some people I even scribbled in their scrapbook to remove the confusion. I guess it would help them.

I was lucky enough to get Hardy's book "A Course of Pure Mathematics" and I never had to worry about such issues. Please get hold of that book to save yourself from the horrors of infinity.


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