MathTeacher
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 Feb11 awarded Popular Question Dec22 comment Should a high school introductory calculus class teach $\varepsilon$-$\delta$ proofs? Yeah, why don't we teach infinitesimals in beg. calculus, now that we have non-standard analysis? Dec22 answered Should a high school introductory calculus class teach $\varepsilon$-$\delta$ proofs? Dec22 answered proof of chain rule Sep24 awarded Autobiographer Jul2 awarded Curious Apr13 awarded Notable Question Mar24 awarded Popular Question Mar11 comment Is there a name to refers to anything that is a point, line, plane, etc? Sorry, I missed the "necessarily" part of Loki's answer. Mar11 comment Is there a name to refers to anything that is a point, line, plane, etc? Ok, but what if they do. In high school language. Mar11 asked Is there a name to refers to anything that is a point, line, plane, etc? Dec11 awarded Yearling Dec8 comment What is a good example to show high school students why a proof for induction is a reasonable kind of proof? I like the subset idea. Dec8 comment What is a good example to show high school students why a proof for induction is a reasonable kind of proof? Yeah but is showing it via induction really the most intuitive way of showing it? At least for me it is not. Dec8 comment What is a good example to show high school students why a proof for induction is a reasonable kind of proof? @John: example 3 was just the sort of thing I was looking for. Can you think of others at about that level? Dec5 comment Why is $\frac{1}{\frac{1}{X}}=X$? Here's another way I look at it: say $x=2$. $1\div\frac{1}{2}$ asks How many one halves fit inside one?" Well, two one halves fit inside one. Dec5 comment What is a good example to show high school students why a proof for induction is a reasonable kind of proof? And I'm going to avoid visual. Many of my students are not comfortable with visual things. Dec5 comment What is a good example to show high school students why a proof for induction is a reasonable kind of proof? The problem with the sum of the first n numbers is that, at least to me, that formula doesn't come to mind by looking at it for n=1, and THEN for n=2, and THEN for n=3 ...and my students already figured out a proof for it non-inductively. I have a similar reservation for the first n squares. Sorry that I am being a pain! Dec5 comment What is a good example to show high school students why a proof for induction is a reasonable kind of proof? I feel like I want something slightly less intuitive than that. At least for me, I don't think mentally that it is true because of induction - instead I think immediately of the curves $y=n$ and $y=2^n$, and based on what we covered, my students probably will too. Dec5 asked What is a good example to show high school students why a proof for induction is a reasonable kind of proof?