Hi guys! You can leave messages for me here.

My previous messageboard has too many comments and images, which cause it to load slowly. If you have a previous conversation please continue it there instead of starting a new thread here.

I will be editing and deleting comments to help keep this loading fast. E.g. Once images are irrelevant, they will simply be displayed as a hyperlink, instead of requiring everyone to download the picture. Irrelevant comments will be deleted.

Please keep conversations separate, IE start a new thread for different comments. This will allow me to easily keep track of live discussions.

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## Comments

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TopNewestCalvin, now this is serious...how am I supposed to find "Calvin Lin's messageboard -4" in the future? Right now, the only way is for me to save the notifications. If any discussion or Note is started, how do we find them again?

Looks like I can try to save problems and notes in "favorites" and use them to save my links to members as well, indirectly. But the Search feature is seriously reduced in utility--I can't use it to find problems, notes, or members that I only have a vague recollection of. I used to use the Search feature all the time, now it's unlikely I'll be using it for anything, except to search wiki subjects.

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To find it type https://brilliant.org/discussions/thread/calvin-lins-messageboard-4-2/ remember -4-2 because someone else first make a note with the same title and Calvin had to write 4 2 and change it back. From where I know this https://brilliant.org/profile/b-n8n5oq/sets/helpful-things/520709/little-help-with-new-brilliant-update/#comment-a3f5136417e92

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I find it troubling that useful options and features are being removed rather than added. Not having the "Follow" option, no longer being able to use the Search function to find members, problems and notes, and no longer being able to "Like" or repost a problem all detract, in my view, from the Brilliant experience and the sense of community I used to feel on this site. (As to the "Followers" issue, I notice that in the "Featured Member" display, even over the last few days, it highlights that a member "has just got followed by their nth Brilliant user"; no doubt this kind of highlight will disappear soon as part of the purge. This display also has highlighted streaks of members, yet in the Stats option there is no longer a list of streaks or points achieved to peruse, again detracting from the sense of community.) The emphasis seems to be directed towards POTW, quizzes and wikis, rather than community and members as it was in the past. (So much emphasis on the POTW appears to me to be siphoning interest from the general community section of problems, so much so that any effort to post problems, notes and solutions that will just languish there, (unless "promoted" to the POTW section, (a la Hunger Games)), has the sense of futility. So there appears to be a change in philosophy being manifested here; perhaps this is more effective in growing the site, but for me it has greatly detracted from its appeal, (although I still appreciate Brilliant and will likely never leave). I'm interested, as always, to hear your thoughts, @Michael Mendrin

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You've hit the problem on the head. I used to be an active member of Yahoo!Answers because for a while it allowed me to keep a close knit community of fellow members, including you. Then for corporate reasons, Y!A deliberately made this difficult, as if they decided they didn't want any "cliques" whatsover, so that one feels isolated in Y!A and out of touch "with the regulars". And that was why I joined Brilliant.org. Now Brilliant.org is going in the same way? Depersonalizing the Brilliant.org experience? Why?

For a while it seemed like Brilliant.org was encouraging the human side of this community of problems, wikis, and discussions, but now the new emphasis is just "problems, wikis, and discussions"--with no faces?

I hope Brilliant.org is just experimenting, and will come up with something better.

As for the seriously truncated Search feature, now it's become much more cumbersome to go back to a problem that I'm working on. I don't understand at all why we can't use Search to locate problems.

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As for the truncated Search feature, the "Recent problems" option does allow one to go back to unfinished problems, although it's not as precise a tool.

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I really hope Brilliant.org is not going in the way of Y!A, losing "its uniqueness and charm" for corporate and marketing reasons.

The "Featured Members" is a step in the positive direction, I hope that's not going to be cut out as well.

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Yes this is going to be a complicated problem. Atleast problems and notes should be added in search engine. Also, if I wanted to solve any problem related to a certain topic I used to find them in the search engine but now it is impossible to find questions relating to a particular topic.

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Comment deleted 5 days ago

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Ram, I'll reprint here my response in the other note:

Brilliant has been evolving since its inception years ago, and I expect it will continue to evolve. I can remember the time it originalily targeted users involved in math competitions to polish their skills, without much sense of community. It's come a long ways from that in response to market realities. Right now, as Silas Hundt has tried to explain, this is about the best allocation of limited resources. Rather than restoring the features which means bringing back old coding, they'll probably do a coding reboot to reduce programming load. Give them some time to come with an improved version, while being aware of the needs of the active 1%. This cannot be done over the weekend.

However, I hope Brilliant will continue to heed Item 5 in Our Principles

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Also the leader board is gone.

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Because there are no followers and following features

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Calvin, thanks for having the Edit choices fixed. Now I find out that the "Like" feature has disappeared. What's the news with that?

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Brilliant is now looking new. Why all these changes are made. No followers No likes No searching for problems and notes. The search for problems and notes should not be removed.

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Also, now the "search machine" can only search for "Wiki Pages" and "Quizzes". We cannot search for members, problems or notes now.

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Yeah, I just noticed that... wow, that's going to make things difficult it's going to make it much harder to find things. What's going on?

As a matter of fact, I wouldn't even be able to find this "Calvin Lin's messageboard -4" at all either! How would I be able to come back to this in the future?

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Also noticed that "following and followers" are gone.

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When we are commenting on discussions or solutions,we sometimes use LaTeX,but we can't preview it before we post it.Can you help with this?Thanks!

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Just post and make edits if there are errors.

If you want a place to type out comments before posting them, then you can use this wiki.

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OK,thank you.

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AFAIK, we can't preview comments.

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Oh,I see.

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A question. When posting solutions or added material to previously posted solutions, is it normal for any such work not "submitted" be lost upon exit? I've had the annoying experience of having spent the better part of an hour developing a solution to a problem (Golden Cubes by W Rose) only to see it vanish while clicking around. I seem to recall that I was able to return to such "work in progress" but maybe my memory isn't right? It has just now happened again.

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Solutions are saved locally to your machine using cookies. Here is a video of it working for a modal popup on the feed.

If that’s not what happens for you, please ensure that you have cookies enabled. If it still remains an issue, can you take a video, or give me detailed steps of what you did such that the solution didn’t appear?

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Actually, things seem to be back to normal? When working on The Strange and Secret Notes of Lovers, I did not seem to be having that problem. But I will keep in mind your suggestions the next time I run into this problem.

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Comment deleted Jan 15, 2017

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I do respect you, and I appreciate the solutions that you've submitted. I do not judge your work lightly. I enjoy reading your solutions because you often get at the underlying concepts to the problem.

When I read a solution, I do my best to point out what I feel are valid concerns / issues / errors. I admit that isn't always right, and when I realize that, I try and make it clear that the concern is not valid (typically by editing the first comment). I do not attack the person, but instead focus on the argument that is made. I do my best to pinpoint any misconceptions / fallacies, but those can be hard to convince another person.

In your case, the most recent example that comes to mind in which we had a lengthy discussion, is with regards to riemann integrable functions, which are similar to, but not exactly the same as, the integral that is taught in most high schools calculus concepts. I think that others who saw the problem and solution discussion, gained a lot from seeing these differences.

Just like complex exponentiation, the complex logarithm is a multi-valued function. What you're essentially saying by "without a pre-established domain", is that we haven't chosen a principle branch. In such a scenario, I default to the "typical" branch (which is the same branch that I take for complex exponentiation), namely

As such, this gives us \( \log_{-6} ( -6 ) = 1 \).

In fact, in this particular case, because the terms are the same (and non-1, non-0), no matter what branch we choose, since the value of \( \ln (-6 ) \) is fixed in our given branch, we have \( \log_{-6} { -6} = \frac{ \ln -6 } { \ln -6 } = 1 \).

More generally, when talking about multiple valued functions, the equality sign means that "there is some value on the LHS that is equal to some value of the RHS". Unfortunately, mathematicians do not distinguish between these and the typical "equality sign means that these are exactly equal".

A common misconception is:

\[ i = \sqrt{-1} = \sqrt{ \frac{ -1 } { 1 } } = \sqrt{ \frac{ 1} { -1} } = \frac{ \sqrt{ 1 } } { \sqrt{ - 1 } } = \frac{ 1 } { i } = - i \]

In this case, if we abandon the principle square root idea, and instead interpret square roots as a multiple-valued function, then by tracking which equality signs are "actual equal terms" vs "equal in the multiple-valued function sense", then you would be able to see how we arrived at such a contradiction.

Explicitly, the equation is saying

\[ i = \{ i, -i \} = \{ i, -i \} = \{ i, -i \} = \{ i, -i \} = -i = -i \]

So, the misconception arises because we're being very sloppy with our notation, and letting the equal sign do double duty.

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No, we cannot (yet) say that \( (-1) ^{ \log_{-1} (-1)^x } = ( -1 )^{ x \log_{-1} (-1) } = (-1)^x \).

Reason being that you're now mixing in a lot of "potential misconceptions", without properly accounting for them other than "These rules were true for real numbers and I'm going to assume that they are true for complex numbers", which often they are not especially due to the "multi-valued nature" of complex exponentiation / logarithm.

In particular, the misconception with complex exponentiation that you're sweeping under the rug is that \( (a^x)^y = a^{xy} = (a^y)^x \). Typially, this is expressed as :

\[ (-1) = (-1)^1 = (-1) ^{ 2 \times \frac{1}{2} } = [ (-1)^2 ]^{ \frac{1}{2} } = 1 ^ { \frac{1}{2} } = 1 \]

Once again, using the language of "equal in the multi-valued function sense", do you see how evaluating the function creates the error?

It is important to check the nitty-gritty details like verifying assumptions, conditions of the theorem, etc. Common examples where people forget about doing so are

Sometimes, people say that this is being "pedantic" or even "stick-up-the-ass". However, you can see why this is important in scenarios like the above. We do have to pedantically checking whether this instance of complex exponentiation is actually valid.

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The comment of "have to pedantically check whether this instance of complex exponentiation is actually valid" is still relevant. This is something that you would have to do, to justify the complex exponentiation step.

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In particular, the misconception with complex exponentiation is that it is not always true that \( (a^x)^y = a^{xy} = (a^y)^x \), especially when \(x, y \) are non-real values. The cases when we have an identity include (but are not limited to)

We have to "pedantically check whether this instance of complex exponentiation is actually valid", and unfortunately neither of these cases apply in the example you wrote, so more work has to be done.

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\[ -1 = (-1)^1 = ( ( e ^ { i \pi } )^ 2 ) ^ { \frac{1}{2} } = ( e^{2 i \pi } )^{ \frac{1}{2} } = 1 ^ { \frac{1}{2}} = 1 \]

So, it is not alway true that \( ( e^x ) ^ y = e^{xy} = (e^y)^x \) for all complex numbers.

If you write up your proof, that might help you identify what assumptions you are making that would indicate why you're having this misconception.

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Can you add your proof of \( ( e^x)^y = e^{xy} = e^{yx} = (e^y)^x \)?

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Points to take note of regarding the statement \( 1 = 1 ^ { \frac{1}{2} } \).

1) If we are "using the main branch of the multivalued logarithmic/exponential function" implies that we are evaluating the function. We evaluate \( \sqrt{1} \times e ^ {i0} = 1 \). So, it is true that

\[ 1 = 1 ^ \frac{1}{2}. \]

However, note that

\[ -1 \neq 1^ { \frac{1}{2} }. \]

2) If we"Consider the multivalued function" means that we're taking equality of multivalued functions, meaning that "one of the values in the set is equal to one of the values in the other set" (which is also why we do not have the transitive value of equality, and hence it doesn't really actually behave like the usual equality sign we're used to). Since \( 1 ^ { \frac{1}{2} } \) is the set \( \{ 1, -1 \} \), hence it is true that

\[ 1 = 1 ^ { \frac{1}{2} }. \]

Furthermore, in this case, we have

\[ - 1 = 1 ^ { \frac{1}{2} }. \]

So, while it ultimately matters whether we're talking about "principle branch evaluation" or "multi-valued functions", it is always true that \( 1 = 1 ^ \frac{1}{2} \).

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Discussion The subject of complex exponentiation is horribly messy, and Calvin has been right in pointing out that many identities that hold elsewhere don't necessarily hold when there's complex exponentiation is involved. Quite literally, the subject branches out everywhere.

Guillermo, for something like this, there should be aLog in to reply

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attempt to explain (one of) the hurdles to \( ( e^x)^y = e^{xy} = e^{yx} = (e^y)^x \) .

Let's continue the discussion here, where ILog in to reply

Is the dress White and Gold, or is it Blue and Black? Please don't start here!

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@Calvin Lin, When I get a community problem wrong and I go back I see that I got it correct (sign) but when I go in they say it is wrong. The same happens when I get a problem correct.

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Can you elaborate on what you mean? Ideally, give me a specific example + screenshots.

Note that "problem of the week" and "community problem" generate different attempts, so for the same problem that appears in 2 areas, you could be correct in one of them and wrong in the other.

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At what date was Brilliant born?

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B D (Brilliant Date) :p

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@Calvin Lin, why do some of the notes do not have the save option but some others (like this one) has the save option?

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Can you give an example (link to note, screenshot) where a note has no save option?

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I am unable to edit this question from quite some days. In fact, there is no "Edit Problem" option. This will happen only when a question is featured in one of the problems of the week. But from last one month I found that this question is not featured and also there is no edit problem option. Why is this happening ?

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For questions that we're featuring (which could be Problems of the Week, on Facebook, in emails, etc), we remove the editing functionality.

I have verified that your linked question is such an example.

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Calvin, I've already asked Brilliant Staff about this. I just now created and posted a dummy problem, and then tried to change the correct answer, either using Edit choices or Edit problem. Neither one would allow me to change the "correct answer", so I'm forced to delete the problem if I happen to need to adjust the answer. That also forces me to change the title of the problem. What's going on?

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Click "More" (down right) and you will see the options save, view reports, toggle latex, edit problem and delete.

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I am saying that I am unable to find the edit problem option when I clicked "More" .

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Is there any wiki for the topic 'Solving Diophantine Equations Using Inequalities'??

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Not as yet. You're welcome to add one :)

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I see that every time in the problems of the week only math's, physics and logical problems are being featured. Why not problems of chemistry and biology are not featured ?

Sometimes I see some good problems of chemistry like this one. I am surprised when I sawed that question has only 129 solvers.

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It's mostly that the quantity and quality of chemistry/biology questions are much lower, which is why they don't make the cut.

I believe we used that chemistry problem on Facebook, which is why it got more solvers than normal (for chemistry problems).

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I have posted a new one. Is this a good one according to your terms of quality and quantity of knowledge it gives.

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Simply saying "exclude this rule" doesn't provide me with enough information to figure out "so what other rules are there that I need to be concerned about?". Looking at your solution, you seem to be making the assumption that electrons are filled in order of increasing energies. (Is this an inherent chemistry rule? doesn't seem like it since the rule is likely the Auf Bau Principle itself.) What in the question implies that they can't be filled in order of increasing orbitals, or even decreasing energies starting with the orbital of highest energy?

E.g. As an extreme example, what you are saying is "Assume that 2 is not the next integer after 1. If so, what is the next integer after 11?" This feels meaningless without knowing much more about the new number system.

Note: I said "quantity and quality of questions", not "quality and quantity of knowledge (in a particular problem)".

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Blake Farrow sir as he is good in writing chemistry problems.

Further I think this question needs assistance fromLog in to reply

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This way, the problem changes from "boring tedious let's see where the electron goes" to "Oh hm, what are the differences in these scientific models, and how can we distinguish them?" (which I believe is much more interesting to the audience).

So, the takeaway is that even if you know there is a specific idea you want people to be aware of, figuring out how to present the problem can have a significant impact on their engagement.

Note In general, it is not good to hide really important information (as opposed to just constant values that are needed) in the details section of the problem.

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this one. If you think any changes are to be made you can do them .

Sir, I have now posted a new question and deleted the before one. Please checkLog in to reply

Extending my example, if we exclude the rule that \( 1 + 1 = 2 \), then what is \( 11 + 1 \)?

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Perhaps che

mistryquestions are somewhatmystery.Log in to reply

They do feature biology problems

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Ok. I saw sometimes biology problems. But did you ever saw chemistry problems.

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one

Finally foundLog in to reply

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here. I hope it is a good one. Actually this is not the question which wanted to post. I had another one but I didn't find a good picture for it so I postponed it.

I have posted a new chemistry problem. See itLog in to reply

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What is meant by

Classical Mechanics?What is the difference between

Classical MechanicsandModern Physics?Is there anything called

Newtonian Physics? If there what is it ?Are the above different branches of physics ?

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I think that all of them are branches of Physics

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Lately, I seem to be experiencing trouble with spacing between paragraphs when posting a problem. After I've spaced the paragraphs in the draft view, and I save it, some of the spacing disappears, and I cannot figure out why. Any idea what could be going on? For example, in When a Mathematician Orders a Slice of Pie, I can't get the comment, "Well, in that case I'll have the [...]" to be spaced from the proceeding paragraph. This sort of thing has happened before.

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In this case, the image needs a new line after it, in order for the "Well, in that case ..." to appear on a new line. I made that singular edit, and it appears correctly now.

I've filed a bug report to understand why this is happening. (I don't know how/why those impact each other)

Let me know if you see this issue on a problem without images.

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When contributing problems,there do exists a biology topic,but those biology problems are not seen in the community page,and people doesn't have a chance to solve it.For example,this one

Can you help with this?

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Ah thanks. I will make the change.

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One of my problems was featured as one of the problems of the week. But there is a difference between the number of solvers in the question part and in the solution part . See the difference between the red part and green part !!!

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That is because we changed the answer options in your question, so these stats will not match up perfectly.

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The first time I did that question,I got it wrong,but at the problems of the week,I got it right.I think this is the reason.

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Yes I too think that is the reason. But they both should be the same know.

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Is there any way to delete set created by oneself ?

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Not currently.

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Every day one of the wikies will be featured as Wiki of the day. My doubt is if a wiki is featured as Wiki of the day can it have chance to be featured as Wiki of the day.

For example, if Arithmetic progression wiki is featured as Wiki of the day can again be featured as Wiki of the day some other time.

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Maybe.

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@Calvin Lin Sir how can we add relevant wiki to our questions.??

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There is an option just above your solution space.

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Shall we get any points for upvotes ?

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No. Points are a measure of your activity, not of your reputation.

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Sir, please answer my below query also.

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Respected Calvin sir can I know how many points we will get if we answer a question with certain level. I want to know how many points we will get on answering each of the 5 levels.

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When you hold the pointer of your mouse on the level(under title) of the problem.

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Yes I came to know about it recently

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Hello sir,

I have started creating some maths problems recently. But they are level 2 or 3. I want to create some tough( level 4 or 5) problems.

Can you please give some suggestions how to create level 4 or 5 problems?…

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@Calvin Lin,

Sir, this is IMO 2017 Day 1 , problem 3. None of the contestant could solve this problem at IMO this year.

Can you tell me the logic and hints required to solve this problem?

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I came across this function and i'd like to ask whether the derivative for it exists.

\[F(x)=\sqrt{\ln\left({\sin{\left(\frac{x^2}3-1\right)}}\right)}\]

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What have you tried?

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I found the range which happens to be equal to zero. The principle domain is just one point \(\dfrac{x^2}3-1=\dfrac\pi 2\).

Since the graph of the function are just points separated by equal distances, is the function differentiable?

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differentiable function? You should be able to check that against the definition.

Good analysis. if you consider this a real valued function with a restricted domain of isolated points, then is it aLog in to reply

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Anything is true of the null set. For example, "All of the mini coopers that I own are blue" and "All of the mini coopers that I own are red" are both true statements because I don't own any mini coopers.

In this case, because the domain is just one point, then the function is trivially continuous and differentiable. Because the definition of these terms are "For any point \(x\) in the domain, there exists a neighbourhood \( N_\epsilon (x) \), such that for any point \( y \in N_\epsilon (x)\), ... ". It doesn't matter what the "..." is, because there is no points \(y\) that satisfies the conditions (e.g. I don't own any mini coopers), and thus the statement is true (e.g. hence all of the mini coopers I own are blue and red).

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When it appears"Discussions for this problem are now closed"? Why does that stop a user to even report a problem? The right to report a problem must be given atleast. I had a little doubt regarding a problem...I wanted to ask...But there is no way that I can even utter that..."Discussions are closed"! Why reports are closed? Just because all the experts have solved it, does that mean that the question is right always? Now you tell me whom should I ask? Particularly I'm talking about this problem:- '3-5-7 square point'. See, I might be proved wrong again by you guys. But that's ok...if there is a mistake from my side, I'll be more than ready to accept it, but kindly make the allowance to express doubts on a problem... And as a user, I ask only this: please provide me with the reason of 'closing the discussion' for the problem after sometime. I hope that you will give me answers to my queries, and I'm sorry in advance if all of this offends anybody here in this site. But I had to ask this... Some of you will already know that I'm kind of a rebel here...I don't want to and mean to be so...It is so because there are a few things I don't understand about this site which I ask...

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We close discussions on problems for various reasons. When we do so, we ensure that the problem is correctly stated, and that the solution explains what is going on. This affects a very small percentage of problems.

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I'm in that small percentage then. But why do you close the discussions? Let it be on... Nothing will happen... Say the problem is correct, solution is also correct. If it's correct, does it mean that nobody is supposed to get a doubt? Everybody is not as brilliant as you, maybe others are, but not me...you must understand that...please...

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Sir, how does a problem gets rated?

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Process by which a problem is rated:

1. The problem creator or moderator gives it an initial seed level. If a problem gets 100++ views, we will also give it a seed level.

2. The community works on the problem.

3. After enough people have worked on it and we have become more confident that the rating is accurate, we will release the level of the problem.

You can help your problems get rated by:

1. Adding a relevant seed level when you post the problem

2. Making it interesting and engaging for others to work on the problem

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OK thanks!

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I'm constantly getting 2 notifications every 10 seconds. But when I click that, it says 'No unread notifications'. Why is that happening? I've clicked that button for about 10 times.

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THanks. We will look into that bug.

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Yeah sure, thanks...

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Calvin, another possible bug report, and I seem to recall this has happened before. Here are 2 problems I solved recently

Golden Cube

Co-co-company

In both cases, I found a better solution, entering a smaller number than the "correct" answer. In both cases, my smaller number was declared, "correct!". Well, this shouldn't be happening, don't you think? Anyway, in the case of the Co-co-company, I believe Marla Reece simply overlooked another way of arranging the 5 circles. However, in the case of the Golden Cube, I actually think W Rose was thinking of another problem than the one I solved. I notice that W Rose does have a tendency not to express his problems clearly.

But, mainly, I'm bringing to your attention that in some of these optimization problems, sometimes when I enter an answer that's different from the supposedly "correct" one, my entry is nevertheless declared "correct". Why do you suppose this happens sometimes?

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For golden cube, you submitted a first answer of 10, which was marked incorrect.

Then, you submitted a second answer, that was slightly smaller than our "correcrt answer". Since it is within the 2% error range of the correct answer, hence it was marked correct.

Similarly with Co-co company, the smaller answer that you submitted was within 2% of the error range, which is why you were marked correct.

For these problems, if you're convinced that your value is correct, please submit a report on the problem. Thanks.

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If you believe that the answer is incorrect, please report it with some justification.

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Oh, I didn't know that Brilliant accepts answers "within 2%". But I've already posted comments in the reports section in both problems, and right now, W Rose seems to be in agreement with me with both the problem statement and the answer. Can the author of a posted problem that has already been answered change his own "correct" answer? If not, then he needs help from the Brilliant Staff to change his "correct" answer.

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Sir, what is the way to post images along posting questions?

Is there any markdown or something else which would help me to draw pictures?

You can see that in all my posts, none of any one posts consists of pictures, geometrical diagrams.

Please help

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When you post a problem, click on "Drag and drop images here or click to upload" located below the question field and just above the preview button.

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sir does wrong answers affect my leveling up?

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Yes. On the stats page, you can see how your ratings change as you answer problems.

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