Eddie, I think your stuff is great. Thank you. :) I love your video on a visual representation of completing the square. Whaddaya think about the following? I believe that f(x) = 1/x as it is typically defined from R\{0} to R is a continuous function, since we make claims about continuity at a point. Because f is continuous at every point in its domain, we can say f is continuous on its domain. Alternatively, we can say a function is continuous at some point in its domain, say z, if its limit at z equals the function value at z. Since there is no function value at 0, because 0 is not in the domain of f, f(0) does not exist. And so we can make no claim of continuity at x = 0. This point, I suggest, is irrelevant. It has nothing to do with f. The domain explicitly excludes it. I presume that this lecture is aimed at high school students. I also teach high school. And I am really interested in helping my students develop understandings that are as close to real mathematics as possible. Continuity is sort of a pet peeve. Now, I don't suggest doing Epsilon Delta proofs with high schoolers. Maybe. I don't know. But I think we can go deeper than whether we pick up our pencil. Especially when it leads to confusion later on when these students take some analysis course and learn that 1/x is continuous. Thoughts? I'd love to chat. Peace and respect, -Andre Rouhani, Arizona, USA
You are really a great teacher Eddie, became ur fan, really :)
You explain really clearly!
Eddie, I think your stuff is great. Thank you. :) I love your video on a visual representation of completing the square.
Whaddaya think about the following?
I believe that f(x) = 1/x as it is typically defined from R\{0} to R is a continuous function, since we make claims about continuity at a point. Because f is continuous at every point in its domain, we can say f is continuous on its domain. Alternatively, we can say a function is continuous at some point in its domain, say z, if its limit at z equals the function value at z. Since there is no function value at 0, because 0 is not in the domain of f, f(0) does not exist. And so we can make no claim of continuity at x = 0. This point, I suggest, is irrelevant. It has nothing to do with f. The domain explicitly excludes it.
I presume that this lecture is aimed at high school students. I also teach high school. And I am really interested in helping my students develop understandings that are as close to real mathematics as possible. Continuity is sort of a pet peeve. Now, I don't suggest doing Epsilon Delta proofs with high schoolers. Maybe. I don't know. But I think we can go deeper than whether we pick up our pencil. Especially when it leads to confusion later on when these students take some analysis course and learn that 1/x is continuous.
Thoughts? I'd love to chat.
Peace and respect,
-Andre Rouhani, Arizona, USA
Ya
@leisure hub lol
Well, you helped me, thanks a lot. And, do you teach physics??