Recent content by David Carroll

Well, I think similar chances held for my ability to learn calculi 1 to 3 (there's some pompous language: pluralizing calculus as "calculi" o0)) and linear algebra. Since I've succeeded so far, I think my chances of mastering analysis should be more optimistic than otherwise.

I'm not that gifted, no. I just assumed that the purpose of a teacher/professor was to help students master the subject matter which already exists in the textbook (unless, of course, it's a class with no textbook). And if I can do that without the benefit of the teacher, more power to me, I...

I think that's what SYoungblood meant: the test doesn't apply because an has to approach zero in order to converge to infinity but that it's not enough (i.e. another test such as the "divergent series minus a finite number of terms"-test), so the test "fails".

Exactly. A zero limit is necessary but not sufficient to determine convergence. Also: this series diverges because it is simply the harmonic series minus the first 33 terms.

Greetings. I just bought a textbook and I have no idea what it is about. A little explanation is in order: One of my goals in life has been to obtain a degree in mathematics. Unfortunately, I have made very poor life choices that have made this goal practically unachievable, which I won't...

Oh, cool.

What am I talking bout, Arnold? I looked back to Larson's Calculus and there was such a proof. I was wrong.

Hello, remy! Would you happen to be French?

My habit is always to go back to first principles. In the case of the derivatives of trigonometric functions, I simply memorized the derivatives of the sine and cosine. I'm not sure what Calculus textbooks you all have used, but the one I went through (Larson, 8th edition) did not give a proof...

I'd prefer rednecks to hipsters any day of the week. And one thing I like about West Virginia: the Liberal Redneck, Which I never knew existed until I came here: "They dayon't lahk Obama because they ahh ray-cist!", which I've heard countless times. Nevertheless, its options for cultural and...

Well, yeah. About the whole "fascist" thing. That might need some clarification. I enjoy being around open-minded, free-thinking people. In my opinion cities like San Francisco and Seattle were great in this regard...till about 20 or 25 years ago or so. About the time that the word...

That last one did it for me. Thank you, FactChecker.

Hmmmm. I'll try. Okay, let Na represent the number of elements of the set A. Let Nb represent the number of elements of set B. Then, if every element of set A is an element of set B it follows that Na is less than or equal to Nb. Also, if every element of set B is an element of set A, it...

DMT. Trust me on this one.

OK, I see. But Houston was listed as the second most ethnically diverse city in the nation according to some on-line report that was published a year or two ago, which I thought was pretty cool. They don't have much of a transit system, though, which sucks.