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Martin Sleziak
Martin Sleziak
12:17 PM
I thought it might be good to have a discussion (or at least some part of it) here. This room is basically about duplicates and related stuff.
I think it would be better if the posts about the same limit were grouped together (even if they are not exact duplicates, for example if they require some specific method, or avoiding some method). For example this limit is three times in one of your lists: math.stackexchange.com/questions/36299/…, math.stackexchange.com/questions/420698/… and math.stackexchange.com/questions/552016/… These 3 occurrences are quite far from each other. — Martin Sleziak 16 mins ago
@MartinSleziak The order is by ad-hoc "hotness points", equal to 20*(total score of answers) plus the number of views. When the same limit appears multiple times, the first appearance should be the canonical one. Rearranging them by hand isn't in my plans; the idea was to make content better accessible with an automatic tool. — Thursday 5 mins ago
BTW some links (probably generated by some automated process) see to be incorrect. For example, one of the answers contains a link like this: $\displaystyle \lim\frac{\sin x}{x}$. It links to question about $\lim\limits_{x\to+\infty}\left(x-x^2\log\left(1+\frac{1}{x}\right)\right)$ (BTW maybe we could move the discussion to chat, so that we do not put too many comments here.) — Martin Sleziak 2 mins ago
@Thursday You write that you do not plan to edit the links by hand. Are you against other users doing it? Would manual editing cause problem for you? (Do you want to replace list by newer automatically generated lists later?)
@MartinSleziak The problem is with that question: the limit that the user is asking about is not found in the question, it's only in the post title. I'll edit. — Thursday 1 min ago
I see, the process you run found $\lim\frac{\sin x}x$ in the body, although the question is about something completely else.
Maybe my main question is: Should I manually edit your posts if I notice problems like above (duplicates, incorrect links)? Or would it be wasted effort? (If you plan to generate new lists later from scratch.)
 
Martin Sleziak
Martin Sleziak
12:34 PM
@AsafKaragila Main reason I went ahead with this is to see what problems will appear with such a list, and thus give more concrete input to discussion in the other thread. This is just an experiment... script time is cheap. — Thursday 15 hours ago
Basically if some users start from your lists and edit them manually, it would also be an experiment showing how much effort would go into improving the lists.
 
Martin Sleziak
Martin Sleziak
12:57 PM
@MartinSleziak They are marked community-wiki. Feel free to edit, though you might find the process pretty slow. After seeing how these look and perform, I don't think I'll keep adding to this thread. Putting also logarithmic limits, exponential, square roots, rational functions... would make browsing next to impossible. I'll try to come up with a better system outside of SE. This thing can sit here as far as I'm concerned. — Thursday 12 mins ago
I will try to summarize my edits here.
I have started by working on limits of $\sin x/x$ from this answer:
2
A: Catalog of limits

ThursdayTrigonometric limits: with sine, at $0$ $\displaystyle \lim\limits_{x\to 0}\frac{\sin x}x=1$ $\displaystyle \lim_{x \to 0} (1+ \sin 2x)^{\frac{1}{x}}$ $\displaystyle \lim_{(x,y)\to(0,0)}\frac{(\sin^2x)(e^y-1)}{x^2+3y^2}$ $\displaystyle \lim_{x \to 0} \sin(x)$ $\displaystyle \lim_{r \to 0} \fra...

This was linking to a post where sin x/x was mentioned, but it was only used to calculate other limit; removed this line: $\displaystyle \lim\limits_{x \to 0} \frac{\sin(x)}{x}=1$
Again in this line the same limit is only mentioned as an auxiliary result used in deriving another limit: $\displaystyle \lim\limits_{u\to0}\dfrac{\sin u}{u}=1$
In this line the limit was used as an auxiliary result, I will move this to another anwer: 1. $\displaystyle \lim \limits_{x \to 0} \frac{\sin x}{x} = 1$
I have moved remaining questions about this limit together, so the first line of that answer looks like this:
$\displaystyle \lim\limits_{x\to 0}\frac{\sin x}x=1$ 1, 2, 3, 4, 5
Now I will have a look at this limit: $\displaystyle \lim_{x\to0}\frac{1-\cos(x)}{x} $
It is the first one from this answer:
1
A: Catalog of limits

ThursdayTrigonometric limits: with cosine (no sine), at $0$ $\displaystyle \lim_{x\to0}\frac{1-\cos(x)}{x} $ $\displaystyle \lim\limits_{x \to 0^+} \frac{\ln[\cos(x)]}{x}$ $\displaystyle \displaystyle\lim_{x\to 0}\frac{\frac{1}{2}x^{-1/2}}{\frac{1}{2}\frac{1}{\sqrt{x}}+\frac{1}{2}\frac{1}{\sqrt{x}}\co...

I have removed this line, since the limit is only used there as an auxiliary result: $\displaystyle \lim\limits_{\theta\to 0} \dfrac{\cos\theta-1}{\theta}=0$
I put other occurrences of this limit together:
$\displaystyle \lim_{x\to0}\frac{1-\cos(x)}{x} $ 1, 2, 3, 4
One more occurrence of the limit $\lim_{x\to 0} \frac{\sin x}x$ which I have missed: math.stackexchange.com/q/98920
 
 
2 hours later…
Martin Sleziak
Martin Sleziak
3:11 PM
This limit also had at least two entries: $\displaystyle \lim_{x\to0}\frac{\cos x -1}{x^2}$ 1, 2
One more duplicate I missed before: $\displaystyle \lim_{x \to 0}\frac{\sin x}{x} = 1$
 

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