Timeline for Best way to teach concept of real numbers using a hands-on activity?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2010 at 14:47 | comment | added | Abhishek Parab | Well, this might not exactly be Real Analysis but possibly interesting to a school child. (I was fascinated as a kid) -- The (binomial) approximation of first two terms to the compound interest formula gives the formula for simple interest. One realizes that higher powers of small numbers can be neglected. | |
| Mar 8, 2010 at 22:05 | comment | added | Harry Gindi | The standard or "complete" reals i.e. $\mathbb{R}$, is constructed by taking the completion of $\mathbb{Q}$ with respect to the standard valuation. The "algebraic reals" is $\bar{\mathbb{Q}}\cap \mathbb{R}$, where $\bar{\mathbb{Q}}$ is the algebraic closure of $\mathbb{Q}$. | |
| Mar 8, 2010 at 21:53 | comment | added | LSpice | fqpc, what does “the algebraic reals” versus “the completed reals” mean? Is it a conceptual difference, an intuitionistic difference, or something else—or do you maybe just mean whether we are regarding the real numbers as forming a field or a topological space? | |
| Mar 8, 2010 at 21:29 | comment | added | Pete L. Clark | @fpqc: +1; what you have now looks helpful. (Note that by "the real numbers", everybody means "the completed reals".) | |
| Mar 8, 2010 at 21:26 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Mar 8, 2010 at 21:16 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Mar 8, 2010 at 21:08 | comment | added | Pete L. Clark | @fpqc: What you say in the comments sounds much more reasonable than in the answer itself. You might want to edit your answer accordingly. In general, when mathematicians are asked for advice on pre-collegiate math ed, it is a big problem if what we suggest is years above the abilities of the average student. This makes us look completely out of touch with the problems that educators are facing. | |
| Mar 8, 2010 at 20:35 | comment | added | Pete L. Clark | "May" be "somewhat" sophisticated? So you think it's possible that discussion of limits, Cauchy sequences and completeness of the real numbers might be appropriate for some middle-school algebra course?? | |
| Mar 8, 2010 at 20:28 | history | answered | Harry Gindi | CC BY-SA 2.5 |