Timeline for Grading a limit problem
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2018 at 2:08 | comment | added | Daniel R. Collins | @StevenGubkin: Disagree. If it's in the selected book, then by default it should be considered as an available definition/theorem/notation usable in student work. For the current question we should assume a base context of defined limits and no extended reals, because that is the common documented practice. For variations the burden of proof is on the OP to represent. | |
| Jan 1, 2018 at 18:08 | comment | added | Steven Gubkin | @DanielR.Collins Many such books also include sections on hyperbolic trig functions. How many courses expect students to know the definitions of these functions? They include "proofs" of all of the major results. How often is understanding of these proofs tested? A curriculum is not determined by the book at all. It is decided by the instructor. | |
| Jan 1, 2018 at 17:15 | comment | added | Daniel R. Collins | @StevenGubkin: Disagree. If that book is selected, it signals that's part of the curriculum. And it's in every such book. | |
| Jan 1, 2018 at 2:25 | comment | added | Steven Gubkin | @DanielR.Collins The fact that it has been defined in the book means very little about whether it is actually part of what students are expected to learn in the course. | |
| Dec 31, 2017 at 23:21 | comment | added | Daniel R. Collins | @StevenGubkin: Disagree. Limits are defined in every freshman calculus book I've ever seen (above examples, etc.) | |
| Dec 31, 2017 at 19:26 | comment | added | Steven Gubkin | @DanielR.Collins The problem is that generally a real number has not been defined, a limit has not been defined, etc. These things happen in a real analysis class. At this level, the justification really is at the level of "big number times a big number is still big". Penalizing someone for writing $\infty \cdot \infty = \infty$ in this context seems weird. When expected rigor is extremely variable, and is adjusted to the whims of the instructor, it seems like rigor is something we do to keep an authority happy, instead of a way to clarify and communicate with others. | |
| Dec 31, 2017 at 19:24 | comment | added | Daniel R. Collins | Because it hasn't been defined in this context. | |
| Dec 31, 2017 at 15:33 | comment | added | Jim Belk | @DanielR.Collins I tend to think that if freshman calculus texts are in contradiction with standard mathematical practice, then the texts are just plain wrong. If a text says "$\infty$ is not a number" and then explains how you can still do arithmetic, I guess that's not too bad. If a text says "you can't do arithmetic with $\infty$" then that's just wrong. In any case, I can't fathom why we would penalize students for doing arithmetic with infinity when this is actually fairly standard notation. | |
| Dec 31, 2017 at 1:42 | comment | added | Daniel R. Collins | Likewise, OpenStax Calculus Vol. 1 does not have the phrase "extended real" anywhere in the text, and says of infinite limits, "We are not asserting that a limit exists." (Sec. 2.2) | |
| Dec 31, 2017 at 1:28 | comment | added | Daniel R. Collins | This argument basically boils down to "infinity is too a number". I would like to see an example of a freshman calculus text that does define the extended reals and its operations. The only example I can lay my hand on (Stein and Barcellos, Calculus and Analytic Geometry, Sec. 2.4) explicitly says, "$\infty$ is not a number". So based on my one data point, it looks like this answer is predicated on directly contradicting one's freshman calculus text. Which would make me very uneasy. | |
| Dec 31, 2017 at 0:52 | comment | added | G Tony Jacobs | Well argued. Unless I had given specific instructions to the contrary for some reason, I think I would do this. +1 | |
| Dec 30, 2017 at 21:49 | history | answered | Jim Belk | CC BY-SA 3.0 |