There was lightning flashing in the distance tonight, but no storm came my way. The last few days have been a time of apocalyptic deluge and dangerous floods, but nothing close to me was damaged or drenched. The weather has returned to the usual balmy soft breath of summer which I love so much. I do my mathematics in the breeze of the air conditioner and desktop fan.

I finished the introduction to tangents and am now working on limits. This is really the first time I have seriously studied them and I am taking great care to familiarize myself with their basic concept and notation. As I said in an earlier posting, I am writing the notation over and over again to make myself used to it. Long ago, back in my college days, I did the same thing with the Greek alphabet and pretty soon those Greek letters will reappear in my math studies.

The idea of limit was known in some way to the ancient Greeks, who knew a version of it as Zeno's paradox where swift-footed Achilles races against the wise tortoise. The paradox involves a sequence of diminishing distances as one progresses, where the distance towards the goal gets smaller and smaller but never reaches the final point. And yet things actually do reach the final point. Hence the need for mathematical limits, to clear up the paradox.

The mathematics site I just mentioned is an exciting find, but I am very annoyed by their misspellings. I find this over and over again: misspellings and typos by brilliant people including science bloggers. I never misspell anythng. It probably means I am not briliant.

The first set of limit problems in the Anton book involve interpreting graphs of functions and naming where the limits are, given the notation for the different sections of the function and their limits. At first I thought that this meant putting a mark on the graph, but that's the artist being misled again. Limits are numbers, so that's what they're looking for. Once I figured that out, I was able to nail down the numbers for the limits, the goals for all those paradoxical journeys, among them the one I am making.

Posted at 2:58 am | link