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1 vote

Should we avoid indefinite integrals?

After having looked into the history of calculus and into original works by Leibniz and others, I have come to the conclusion that the schizophrenic way the "indefinite integral" is ...
  • 291
1 vote

Is this motivation for the concept of a limit a good one?

Two points to think about: It might be more intuitive to replace "from some $N$ onward" by "for all $n$ except finitely many". I often present the notion of a limit through a game:...
3 votes

Is this motivation for the concept of a limit a good one?

Here is a simpler definition of limits which works better for monotone sequences, and has value in motivating further investigation of the concept of limits: If a sequence $x_1, x_2, ...$ is ...
  • 241
3 votes

Is this motivation for the concept of a limit a good one?

While monotone behavior is important in analysis (such as the monotone convergence theorem in measure theory), I think you should forget the emphasis on monotone behavior and just be honest with the ...
  • 2,433
7 votes

Is this motivation for the concept of a limit a good one?

I don't like it. Had a hard time following it. Just tuned out. Yes, I'm not a Ph.D. in math. But neither will be the target students. You should have won me over. You didn't. I have the IQ to ...
  • 189
9 votes

Is this motivation for the concept of a limit a good one?

The concept of a limit has nothing to do with the order on $\mathbb{R}$. The standard definition of a limit of a sequence generalizes, almost verbatim, to sequences with values in $\mathbb{R}^n$, ...
  • 954
3 votes

Is this motivation for the concept of a limit a good one?

I think the answer depends on the meta question: why are students learning the definition of a limit? Here are some reasons I can think of: Because students are taking an intro-to-proofs class and ...

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