New answers tagged concept-motivation
1
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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 ...
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1
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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:...
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3
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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 ...
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3
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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 ...
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7
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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 ...
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9
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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 $\mathbb{R}^n$, ...
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3
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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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