Mathochism: In the neighborhood?

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Under the compass of Damocles We continued our discussion on limits today, and applied them to intervals defined by epsilons in the y axis and their relationships to deltas in the x axis.

I remember covering this during the spring, and not being particularly befuddled by it. But after going over the material this time, the professor told us this was one of the hardest concepts in calculus. Is it? Maybe I’m really not getting it, then.

Here is my very non-mathematical take on limits: I’m driving my car down a freeway, heading for a specific destination. Suddenly, traffic comes to a screeching halt. Now, whether my journey continues depends on what made traffic stop. In the best case, it’s just an obstacle in the road, like, say, a couch. After the CHP removes it, we can get moving again! (Can you tell this may have actually happened to me at one point, say on the 405?)

Some obstacles, however, are insurmountable. If a sinkhole the size of the Grand Canyon suddenly appears ahead of me (and hopefully doesn’t suck me in) I’m out of luck, because my flying car is in the shop (damn you, 007, and your crappy driving skills). I’m not getting to my destination that day, and need to go back and find another freeway.

In other words, couch = function I can finagle so that I can find a limit (albeit one where the graph has a hole). Grand Canyon = function where the two-sided limit does not exist. Sure, I can peer into the Grand Canyon from either side, and get as close to the edge as I dare without falling in. But since my flying car is not accessible, that’s all I can do.

So the idea of intervals, or neighborhoods, as my calculus professor calls them, makes sense. How close to the obstacle can I go? 10 feet? 3? Mathematically, I can get infinitely close, and how close I get on one side is not necessarily as close as I want to get on the other side.

It seems fairly clear to me. But maybe I’m just fooling myself, and I’m not even in the right neighborhood.

All text copyrighted by A.K. Whitney, and cannot be used without permission.

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