12.5 due April11

This is my LAST reading assignment for a math class EVER. At BYU. Who knows. Maybe I'll go on to get a masters degree is math someday. For now, though...this is it. What a bittersweet moment.

Continuity is a condition we have been discussing in class. We have had to be pretty careful because you can't say that x is in a certain range that covers the function at a point where it isn't continuous. So now we have defined the three conditions which must be satisfied for a function to be continuous at a certain point. The third condition (to me) is really the only necessary condition. Because if the limit as x-->a = f(x) = f(a), then that implies that the limit exists and that f is defined at a. But I guess we can go step by step if math says so.

Continuity is proving to be harder than expected. I guess because I figured all we had to show was that the limit exists. Which is true, but to match it up with the function is harder. Essentially we need the limit and the point in order to say that they are continuous, and I get it now... Just because there's a point there doesn't mean there were points before that one that lead up to it (the limit) and just because all the points are leading up to it doesn't mean that there's a point there. Fun.