Timeline for Dividing by zero
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2015 at 4:19 | comment | added | Jared | I'm seriously not understanding the criticisms here, because I am hearing: 1) "It's possible to extend the real numbers in various ways, some of which make dividing by 0 meaningful"--I said this by saying: "it can be either ±∞ (it's not clear if it's positive or negative without further context)" and 2) "Your answer is incorrect, however, in suggesting that one or the other is always possible" yet I said: "On the other hand, if you try to divide $\frac{0}{0}$ then the answer is indeterminate--it could range from ±∞ to some finite value (including 0) to the limit does not exist at all." | |
| Oct 27, 2014 at 3:53 | comment | added | Jared | I think saying that I am claiming that dividing by zero (of a finite number) always results in either $+\infty$ or $-\infty$ is reading a lot into my statement (however, I will grant that it's not totally clear). I made the statement that which ($+\infty$ or $-\infty$) it is, isn't clear without further context (the context I had in mind was is it a left-handed limit, right-handed limit, or does it converge to one or the other from both sides). I suppose I should have further elaborated on that point, but I don't see much point now. | |
| Oct 27, 2014 at 1:25 | comment | added | Andrew Sanfratello | @Jared, I am responsible for the down vote. I think the comments above by Henry Towsner reflect the problems that I had with this answer. I understand that in a Calculus environment that relating $\frac{n}{0}$ for $n\neq 0$ to $\pm\infty$ can be useful, but you did not clarify this at the outset in your answer. | |
| Oct 26, 2014 at 14:56 | comment | added | Henry Towsner | More importantly, it isn't appropriate to assume that the two-point compactification is always the right extension to think about. The right way to extend the real line for working with division by 0 is situational; saying that it involves thinking about limits is assuming a context that wasn't given in the question. | |
| Oct 26, 2014 at 14:54 | comment | added | Henry Towsner | Your answer is incorrect, however, in suggesting that one or the other is always possible: plenty of limits of the form $\lim_{x\rightarrow a}\frac{n}{f(x)}$ where $\lim_{x\rightarrow a}f(x)=0$ can't meaningfully be assigned either $+\infty$ or $-\infty$ as an answer. | |
| Oct 26, 2014 at 14:52 | comment | added | Henry Towsner | I'm not responsible for the downvote, but I agree that this isn't a very good answer. It's possible to extend the real numbers in various ways, some of which make dividing by 0 meaningful (or sometimes meaningful); on the projective line (i.e. the one point compactification), dividing by 0 (other than 0/0) just gives the unique point at infinity. On the two-point compactification, some divisions by 0 meaningfully give either $+\infty$ or $-\infty$ as an answer. | |
| Oct 26, 2014 at 8:57 | comment | added | Izkata | A comment on your comment: This isn't StackOverflow at all, it's the Math Educators site on StackExchange. Don't know about the downvote, though | |
| Oct 26, 2014 at 6:01 | comment | added | Jared | I would appreciate some feedback on the downvote. I am fairly new to this section of stack overflow, so I'm sure I've given bad advice, but I do not see what is necessarily wrong here. | |
| Oct 26, 2014 at 4:27 | history | edited | Jared | CC BY-SA 3.0 |
added 358 characters in body
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| Oct 26, 2014 at 4:21 | history | answered | Jared | CC BY-SA 3.0 |