Timeline for What books properly address the properties of $a^b$?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Sep 22, 2020 at 20:26 | history | edited | Ted Ersek | CC BY-SA 4.0 |
I added one more property and edited a few to make them more general.
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| Mar 24, 2019 at 6:55 | comment | added | Daniel R. Collins | Note that there are multiple answers in the thread I linked above that argue a clause like "all quantities are defined [real]" is insufficient to make these properties well-defined. | |
| Mar 23, 2019 at 20:08 | history | edited | Ted Ersek | CC BY-SA 4.0 |
Revised the last paragraph of my previous edits.
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| Mar 23, 2019 at 20:01 | history | edited | Ted Ersek | CC BY-SA 4.0 |
Revised the last paragraph of my previous edits.
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| Mar 23, 2019 at 17:49 | comment | added | Dave L Renfro | @user52817 has pointed out that the CRC case doesn't appear to qualify as an error, and it seems pretty evident to me that the Larson, et al. case is an editing oversight (because all the examples involve positive bases; if this assumption is stated on the p. 330 cited, then it's definitely an editing oversight). | |
| Mar 23, 2019 at 15:15 | comment | added | user52817 | In your CRC example, we are to assume all quantities are real. For example, with $\sqrt[x]{ab}=\sqrt[x]{a}\sqrt[x]{b}$ we must assume the quantities $\sqrt[x]{a}$ and $\sqrt[x]{b}$ are real. So the text is not incorrect. | |
| Mar 23, 2019 at 15:00 | history | edited | Ted Ersek | CC BY-SA 4.0 |
Added comments at the end
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| Mar 23, 2019 at 14:26 | history | edited | Ted Ersek | CC BY-SA 4.0 |
added 1750 characters in body
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| Mar 19, 2019 at 16:26 | comment | added | Daniel R. Collins | People disagree about some of those properties (most notably: along the real vs. complex analyst axis). Related: math.stackexchange.com/questions/1628759/… | |
| S Mar 18, 2019 at 13:24 | history | suggested | amWhy | CC BY-SA 4.0 |
corrected duplication, formatting
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| Mar 18, 2019 at 10:15 | comment | added | Gerald Edgar | Maybe the only books that correctly discuss $a^b$ (in your sense) are textbooks in complex analysis. | |
| Mar 17, 2019 at 10:23 | comment | added | Dave L Renfro | Pretty much every intermediate algebra, college algebra, and precalculus text I've ever taught out of (going back to 1983) gives the appropriate restrictions for these properties to hold. Also, most books I've taught from explicitly state that $\sqrt{x^2} = |x|.$ I could provide you with titles of dozens of such books on my bookshelves (not all of which I've taught from), with specific page references, but I don't see the point, because you could browse the shelves of any college/university library and find the same. Perhaps of more interest might be which texts DON'T do this. | |
| Mar 16, 2019 at 23:25 | review | Suggested edits | |||
| S Mar 18, 2019 at 13:24 | |||||
| Mar 16, 2019 at 22:13 | comment | added | Xander Henderson♦ | I am not sure that I agree with your assertion that every student needs to know when these properties can be extended to the complex numbers, since I am not entirely sure that I agree that every student needs to know much of anything about complex numbers. I think that the more important thing to do in this case is to very carefully emphasize the hypotheses of the theorem(s) at play here. For example, for any positive $a$ and $b$, we have $\sqrt{ab} = \sqrt{a}\sqrt{b}$. Emphasize the necessity of positivity by watching what goes wrong with $\sqrt{-1}\sqrt{-1}$. | |
| Mar 16, 2019 at 21:08 | history | edited | user507 | CC BY-SA 4.0 |
mathjax in title
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| Mar 16, 2019 at 19:31 | comment | added | JTP - Apologise to Monica | Are you literally asking for book titles, or the general description of the math course? | |
| Mar 16, 2019 at 18:19 | comment | added | Ted Ersek | @Joel Reyes Noches, The target audience would include the better high school students. Also those in the first two years at a university and are taking a lot of math courses. | |
| Mar 16, 2019 at 18:12 | history | edited | Ted Ersek | CC BY-SA 4.0 |
Added a sentence about extending the properties to complex numbers.
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| Mar 16, 2019 at 3:18 | comment | added | JRN | Who are the target audience for the books you are looking for? High school students? Undergraduates? | |
| Mar 16, 2019 at 1:21 | history | asked | Ted Ersek | CC BY-SA 4.0 |