User talk:Wcherowi/Archive 6
This is an archive of past discussions with User:Wcherowi. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 4 | Archive 5 | Archive 6 |
Editing Catenary
Hello, recently you removed what I added to the Catenary page. I am very new to this, would you mind elaborating on the reason for the removal? Legoatoom (talk) 18:49, 26 May 2020 (UTC)
- One of the hardest things for a new editor to get their heads around is Wikipedia's policy of no original research. This is one of the fundamental rules for editing Wikipedia, known as the five pillars. We do not put up new information, only information that has already appeared in a reliable source. This might seem a little harsh, but it is the only way to maintain Wikipedia's reliability. Unsourced material is regularly removed if there is even a hint of it being an editor's own work. I hope that you are not too discouraged by this first setback and will try again to post something with an appropriate source. --Bill Cherowitzo (talk) 19:09, 26 May 2020 (UTC)
- Thank you for explaining this and keeping the website reliable. I would like to know how I should have done the source as I created the function myself. Legoatoom (talk) 19:21, 26 May 2020 (UTC)
- I'm afraid that there is no hope for this at present. You would have to get the result published in a reliable publication before we could use it in Wikipedia. --Bill Cherowitzo (talk) 20:04, 26 May 2020 (UTC)
- Thank you for explaining this and keeping the website reliable. I would like to know how I should have done the source as I created the function myself. Legoatoom (talk) 19:21, 26 May 2020 (UTC)
Unit Circle Removed Changes
Hi, you removed the Unit Circle sammary image I've added. Many people fail exams because of lack of such sammary on Google searches. It's a very common topic in many school tests and academic courses.
I saw you commented there is no link to resource. So first of all, I added a discussion prior to making the changes. Why undo someone's work and not leaving a comment asking for proper sources if that's the problem?
Secondly, you want me to add the sources in order to undo the undo?
Best regards,
Vitalipom
— Preceding unsigned comment added by Vitalipom (talk • contribs) 12:51, 1 June 2020 (UTC)
- @Vitalipom: The protocol on Wikipedia talk pages is to add new material to the bottom of the page (this is not common in the rest of the web). I have taken the liberty of moving your comment here, I hope you don't mind.
- While you did initiate a discussion of this on the appropriate talk page, the lack of responses should have told you something. Your serious confusion of basic concepts made it hard for editors to react in a meaningful way. One could distinguish between unit circles in the Euclidean plane and the complex plane, but the definition remains the same in either setting. The three functions you mention do not define different unit circles, they are only used to express the coordinates of the points on the unit circle in different ways. If you actually found sources for your point of view, you should probably throw them away as being useless.--Bill Cherowitzo (talk) 18:26, 1 June 2020 (UTC)
The image I added might help people learn for their exams more efficiently. Where can add to be findable and in appropriate context? Vitalipom (talk) 18:32, 1 June 2020 (UTC) @Bill Cherowitzo: not sure if I know how to tag Vitalipom (talk) 18:34, 1 June 2020 (UTC)
- Perhaps I did not make myself clear enough. The images you posted are wrong! You have given cartesian coordinates of some points on various curves, but in no case do these points lie on a circle (unit or otherwise). At the very least, these diagrams are misleading and would do considerable harm to anyone using them to study for an exam. If your intent was to use them as a mnemonic device, they seem to me to be too cluttered to serve that purpose.--Bill Cherowitzo (talk) 19:23, 2 June 2020 (UTC)
Bill Cherowitzo oh I see, you're saying that sin(2pi) has nothing to do with the Unit Circle, well then you're not right. sinus(teta) is the relation in the triangle which's angle teta and hypothenuse is 1 (one unit). Now look what you did. You reverted my work, deleted twice something that someone else did. You are not aware of this material and apparently you need these schemes more than the students to whom I uploaded it because you publicly call yourself Mathematician on Wiki pages. And finally you prevented thousands of pupil not less smarter than you to prepare for the exam. — Preceding unsigned comment added by Vitalipom
Twitter ratio
Afraid I do not understand the reason for your revert. Can you elaborate? --Webmgr (talk) 05:00, 8 June 2020 (UTC)
- As I review that edit I can see that I was being a bit hasty. The "See also" section is meant to link to other articles that will expand on the topic; go into some detail in more depth or provide a different viewpoint. My initial reaction was that this was just a name that had "ratio" in it and so it didn't belong. I was wrong in this assumption, but I'm still not convinced that it belongs in this section as it does not provide any new information about ratios. It would be more appropriate to put the link into a section about applications or popular usage.--Bill Cherowitzo (talk) 18:21, 8 June 2020 (UTC)
Invitation to RedWarn
Hello, Wcherowi! I'm Ed6767. I noticed you have been using Twinkle and was wondering if you'd like to beta my new tool called RedWarn, specifically designed to improve your editing experience.
RedWarn is currently in use by over 80 other Wikipedians, and feedback so far has been extremely positive. In fact, in a recent survey of RedWarn users, 90% of users said they would recommend RedWarn to another editor. If you're interested, please see the RedWarn tool page for more information on RedWarn's features and instructions on how to install it. Otherwise, feel free to remove this message from your talk page. If you have any further questions, please ping me or leave a message on my talk page. Your feedback is much appreciated! Ed6767 talk! 19:10, 16 June 2020 (UTC)
Vieta jumping
You undid my changes in Vieta jumping and called them "wholesale conversions" and mentioned several reasons for not doing that. I am keen on getting to know them, because those changes took some time. — Preceding unsigned comment added by Tangentialvektor (talk • contribs) 18:07, 25 June 2020 (UTC)
- This issue has been discussed many times over the years. Let me point you to MOS:FORMULA, which summarizes some of the pros and cons. Basically though, the advice there can be simply put as "if it ain't broke, don't fix it".--Bill Cherowitzo (talk) 18:53, 25 June 2020 (UTC)
Reverting use of upright in Algebra.
I doubt using upright=scaling factor
"destroyed illustrations" unless you are using an uncommon browser or display. Help:Pictures recommends using upright to allow user preferences to determine image size. In fact, MOS:IMAGES states:
- Except with very good reason, a fixed width in pixels (e.g.
17px
) should not be specified. This ignores the user's base width setting, soupright=scaling factor
is preferred whenever possible.
- The 1st image was narrowed by 4 px, probably unnoticable. In fact if this is true: "The exact width is computed by starting with the default thumbnail width, multiplying it by scaling factor, and rounding to the nearest multiple of 10", using the normal default width of 220px with an upright=0.8 would result in an image 180px wide.
- The 2nd was reduced by 44px, definitely noticable. Help:Pictures also states "The default behavior can make a tall, thin picture come out too large." I felt the picture was too large and scaled it down. If you feel the full width is warranted, remove upright=0.8.
- The 3rd was narrowed by 24px, again noticable. It should be the same width as the one above. 200px is equivalent to upright=0.9.
- The 4th was widen by 11px. This was done to make the narrowed images a consistent width and to comply with the MOS:IMAGES warning:
I hope I have explained my rational for the edits sufficiently. User-duck (talk) 21:29, 12 July 2020 (UTC)
Sorry, my error. Due to slow speed in opening the page the images didn't appear as I scrolled down the page and I assumed that it was due to the edit you just made. Again my apologies for a bad revert. Bill Cherowitzo (talk) 23:23, 12 July 2020 (UTC)
Copying within Wikipedia requires attribution
Thank you for your contributions to Wikipedia. It appears that you copied or moved text from Sphere into Pencil (mathematics). While you are welcome to re-use Wikipedia's content, here or elsewhere, Wikipedia's licensing does require that you provide attribution to the original contributor(s). When copying within Wikipedia, this is supplied at minimum in an edit summary at the page into which you've copied content, disclosing the copying and linking to the copied page, e.g., copied content from [[page name]]; see that page's history for attribution
. It is good practice, especially if copying is extensive, to also place a properly formatted {{copied}} template on the talk pages of the source and destination. Please provide attribution for this duplication if it has not already been supplied by another editor, and if you have copied material between pages before, even if it was a long time ago, you should provide attribution for that also. You can read more about the procedure and the reasons at Wikipedia:Copying within Wikipedia. Thank you. If you are the sole author of the prose that was moved, attribution is not required. — Diannaa (talk) 12:53, 18 July 2020 (UTC)
Disambiguation link notification for July 20
An automated process has detected that when you recently edited Latin rectangle, you added a link pointing to the disambiguation page Fixed point (check to confirm | fix with Dab solver).
(Opt-out instructions.) --DPL bot (talk) 06:18, 20 July 2020 (UTC)
Happy First Edit Day!
Happy First Edit Day!
Invitation to join the Ten Year Society
Dear Wcherowi/Archive 6,
I'd like to extend a cordial invitation to you to join the Ten Year Society, an informal group for editors who've been participating in the Wikipedia project for ten years or more.
Best regards, Chris Troutman (talk) 13:00, 10 August 2020 (UTC)
You reverted the changed I made on the page about the geometric series
The geometric series section on repeating decimals was incorrect, even listing the formula incorrectly as (a/1-r) equaling the sum of r^n with respect to n, when it already acknowledged that the series is instead equal to a-r^n/1-r. You must include the infinitesimal difference in expressions of infinitesimals.
- There is no number "n" in 0.7777..., which is an infinite sum equal to (not approximately equal to, or essentially equal to) 7/9. Per WP:BRD, do not restore your edit without consensus; but there will not be consensus for introducing a fringe view about the meaning of decimal notation to the article. --JBL (talk) 17:38, 13 September 2020 (UTC)
- Thanks JBL I couldn't have said it better myself.--Bill Cherowitzo (talk) 21:30, 13 September 2020 (UTC)
- To say .7 repeating equates to 7/9 is foolish. The fact that it goes to the bounds of infinity with 7*10^-n as n approaches infinity accounts for infinitesimals, and yet you say infinitesimals are equal to 0. What's the limit of .9 repeating ^10^n as n approaches infinity? 1/e. What's the limit of 1^10^n as n approaches infinity? 1. You acknowledge infinitesimals in your infinite summation, and then say they don't exist. Which is it? Do you do the same with complex numbers? Do you say 1+i is exactly equal to 1? Approaching does not mean equal.
- Infinitesimals do not exist in the field of real numbers as they do not satisfy the Archimedean property. If you want to include them, then you are not talking about real numbers and are indulging in non-standard analysis. This is all well and good, but please learn the subject before subjecting me to more of your prattle.--Bill Cherowitzo (talk) 19:57, 15 September 2020 (UTC)
- You are correct in that they do not exist in the field of real numbers, but neither does .9 repeating. One can't just express a number with an infinitesimal difference and then say that, since infinitesimals don't exist in real numbers, that it's equal to the original number, with no difference. The geometric series here HAS an infinitesimal if you create in infinite sum. Not only is one subtracted, there are also infinitely many added to make the repeating number. Here's an analogy. e^ix = cosx + isinx. You are essentially saying e^ix = cosx because i isn't real. You include nonstandard analysis by creating a repeating number and using the geometric series to an infinite value, and then ignore a part of nonstandard analysis by saying it's not real. Call it whatever you want, you still included infinitesimals, and then ignored others. Bigparsely (talk) 20:22, 16 September 2020 (UTC)
Edit integration by substitution
You reverted two edits I made on the article on Integration by substitution. I believe the edits were correct and would like to see if we can agree.
In the statement of a theorem concerning subsitution in definite integrals and its proof, the formulation "if u = φ(x)" occurred. I submit that even if we may say something like that when explaining to beginner students, it actually makes no sense. The integral is some number by the definition of the Riemann integral, and equally , being the integral over the function f on the interval , is some number. The content of the theorem is then that these numbers happen to be equal. Note that we could equally well state
Would you explain that by saying ?
MathHisSci (talk) 20:45, 27 October 2020 (UTC)
It is a very tortured way and also it is stated when it is said there "in general they are not permutations" Check the formula k^n as is all the possible tuples made with the elements of a second set. The decimal numeric system is an example: you have a set of 10 symbols 0..9 so all the possible 3-tuples from the set 0,1,2,...,9 are 000,001,002,003,010,011,012,...,999 so 10^3 tuples is only the plural of tuple: ordered list. The least to do to clarify is change tuples to tuples of set S Orendona (talk) 22:26, 1 November 2020 (UTC)
The problem is that Permutations with repetition are not permutations. That also is stated in the article, It is a probability scalar number as it is used Orendona (talk) 11:23, 4 November 2020 (UTC)
https://www.ck12.org/probability/permutations-with-repetition/lesson/Permutations-with-Repetition-BSC-PST/#:~:text=There%20is%20a%20subset%20of,of%20objects%20that%20are%20identical. https://brilliant.org/wiki/permutations-with-repetition/ https://www.mathsisfun.com/combinatorics/combinations-permutations.html https://www.google.com/search?q=Permutations+with+repetition&oq=Permutations+with+repetition&aqs=chrome..69i57j0l4j69i60l3.9800j0j1&sourceid=chrome&ie=UTF-8
— Preceding unsigned comment added by Orendona (talk • contribs) 03:54, 9 November 2020 (UTC)
ArbCom 2020 Elections voter message
Catenary contribution deletion
Hello, why did you delete my contribution? My solution is valid and verified by faculty peers. If you have any mathematical or logical criticism, please elaborate. If not, please do not strike down with no reason. — Preceding unsigned comment added by R.zalman (talk • contribs) 21:04, 2 February 2021 (UTC)
- Your solution was unsourced as I mentioned in my edit summary. Wikipedia does not publish original work (see WP:NOR), so no matter how correct the solution was, it can not be used until it is published in a reliable source.--Bill Cherowitzo (talk) 22:52, 3 February 2021 (UTC)
Percentage point
Dear Wcherowi, The changes I made you reverted as "good faith edit". However, I'm afraid that the current definition of the percentage point may be interpreted in the way that 44% - 40% = 4% is wrong. Of course, it is 4 percentage points as well. I am not against "percentage points". However, from the mathematical point of view, the arithmetic difference of two percentages is the value in percentages again. So, I wanted to ask why did you revert my contribution? I'm looking forward to your reply, so I can improve my contribution. ToMiBi (talk) 16:43, 5 February 2021 (UTC)
- The whole idea of introducing the term "percentage point" is to avoid the confusion that you are trying to introduce. Percentage points are not percentages. Your insistence on saying that m% - n% = (m-n)% is just a meaningless manipulation of symbols. While it is true that you can express a percentage point as a percent, it is not given by this simple-minded formula. A change from 1% to 5% is a change of 4 percentage points, but an increase of 400% (and not 4% as you would like to say), and the example in the article, from 40% to 44% is likewise a 4 pp increase, but a 10% increase. You can not equate percentage points with percentages because the percentages depend on the magnitude of the quantities and the percentage points do not.--Bill Cherowitzo (talk) 23:29, 5 February 2021 (UTC)
The water level indicator displays the water level in a rainwater tank from 0 to 100%. It corresponds to the volume of water divided by the volume of the rainwater tank. Let's say (due to the rain), there is a change of water level from 1% to 5%. I agree that the volume of water has relatively increased by 400%. However, it is still true that the water level has increased by 4%, since water level is defined as the volume of water divided by the volume of the rainwater tank. And that volume of new water corresponds exactly to 4% of water level change. In other words, if the total water volume divided by the tank volume is 5%, could you explain why the new/added water volume divided by the tank volume is not 4%???
So, the problematic part is not the percentage itself, but 1) expressing what is a base of percentages, 2) providing the information if the increase is expressed as a relative change (fold change) or as a difference (absolute change or actual change).
Wikipedia says: "For example, moving up from 40% to 44% is a 4 percentage point increase, but is a 10 percent increase in what is being measured."
To me, it is not clearly defined what is being measured... "The water volume or the water level"? It is a relative increase or an absolute increase? Moreover, if 40% + 4 pp = 44%, then for sure it implies that 4 pp = 4% (otherwise we cannot sum up these numbers).
I hope you can see my point. ToMiBi (talk) 19:41, 7 February 2021 (UTC)
- No, no. You are making the same mistake in different terms. Percentages do not add or subtract as their numerical values. A simple example will show this. Suppose you have 100 ml. of milk that is 30% cream, and 100 ml. of milk that is 50% cream. Add the two together and you have 200 ml. of milk that is 40% cream (and not 80% cream, as you would have it). Another example shows that you can not use a simple additive rule without taking into account the total volumes. Again, 100 ml. of 30% milk and now 300 ml. of 50% milk. Combined this gives 400 ml. of 45% milk.--Bill Cherowitzo (talk) 20:43, 8 February 2021 (UTC)
I completely agree with your example. There is no discussion about that. Or are you suggesting that I can use percentage points instead? I.e. add or subtract p.p. as their numerical values? In that case I do not agree with you (200 ml. of milk that is 80 p.p. cream makes no sense to me). Moreover, my example is telling a different story. You basically said that I'm not taking into account the total volumes. Ok, let's fix this. If rainwater tank volume is 100 liters and there is just 1 liter of rainwater, then the volume of rainwater corresponds to 1% of the tank volume (water level indicator displays 1%). If due to the rain, there is a 4 liters increase, then there are 5 liters of rainwater in total. Thus, new water level corresponds to 5% of tank volume (and the water level indicator displays 5%). So, could you explain, please, why the new/added water volume divided by the tank volume is not 4%? ToMiBi (talk) 14:25, 9 February 2021 (UTC)
- (talk page stalker) For a 100 L barrel that originally has 1 L of fluid in it and then later has 5 L of fluid in it, the following things are all true:
- The water level has increased by 400%.
- The water level has increased by 4 percentage points.
- The water level has increased by 4% of the volume of the tank.
- The last two statements are synonymous, the first is not synonymous but is equivalent in this particular example. I agree with Bill that your addition to percentage point did not improve the article. --JBL (talk) 15:00, 9 February 2021 (UTC)
- Dear @JayBeeEll:, I really appreciate your reply. Thank you. OK then. Let's find the way to say that 1) if clearly defined, the p.p. is synonymous to the percentage (see your last two statements) and 2) everyone should be aware of what is being measured (see the definition on Wiki and your very first statement: 400% of what? If not spoken, it could be "... of the volume of the tank". To me, the change from "The water level has increased by 400%." to "The water level has relatively increased by 400%." makes a huge difference, since, the relative increase is expressed as a ratio, where the denominator represents an old value - and that defines the basis for the percentages.) May I ask you to clarify the definition on wiki, please? Maybe I am not the best person for that. But at least I can see that the current definition has flaws. ToMiBi (talk) 19:25, 9 February 2021 (UTC)
the p.p. is synonymous to the percentage
No: as Bill has explained several times, p.p. is the unit of measurement of a change in a percentage. The true statement is that some (but not all) uses of the words "percentage point" can be rephrased to not use those words, by referring to an absolute change whose size is a percentage of some other quantity, as in the 3rd bullet point above. But there are also examples (Bill has offered several) where no such substitution is possible.To me, the change from "The water level has increased by 400%." to "The water level has relatively increased by 400%." makes a huge difference
I understand that you believe there is a difference between those things, but that is because you are confused. Percentages are always relative measures; the phrase "X increased by 400%" always means "... by 400% of its previous value". The existing definitions are completely fine; it is your preferred interpretations that are in error, and once you adjust them, everything will be ok. --JBL (talk) 19:43, 9 February 2021 (UTC)- Dear @JayBeeEll:, DIN 5477 standard (in german) explicitly recommends avoiding the term percentage point in order to avoid ambiguities and misunderstandings. Instead, the text or formula symbols should be used to clearly distinguish the difference between the ratios (relative changes) and the relative differences. So I think I have a significant group of people on my side with a different perspective. The true statement is that all uses of the words "percentage point" can be rephrased to not use those words! Actually, there is no real need for the term percentage point (from the mathematical point of view). The term percentage point is just a linguistic tool to express something briefly. It is very often used in economics. But economics is not the only discipline in the world. I just hope you don't claim that the DIN 5477 standard is wrong and everyone who doesn't use percentage points is confused. Please take a few minutes to look at this situation from this new perspective. Then you can go back to yours. Sincerely, ToMiBi (talk) 21:52, 9 February 2021 (UTC)
- I do not know what "DIN 5477" means and do not have any idea why you think it is relevant here. This is the English wikipedia; in English, "A change of d percentage points" is completely unambiguous. Maybe in German this is not the case (I have no idea), or maybe DIN 5477 (whatever that is) is wrong. I don't see why that should be surprising. Certainly, I have seen instances of people trying to make changes based on ludicrous ideas like IEEE standards for how to write the number "e" are binding on wikipedia, and those always (and correctly) get repelled; the idea that we should follow standards from some non-Anglophone organization is even sillier. There is definitely a participant in this discussion in need of absorbing a new perspective, but I am afraid you have mis-identified who it is. --JBL (talk) 22:21, 9 February 2021 (UTC)
- Dear @JayBeeEll:, It is no matter of language. In our country 1+1=2. Maybe in the UK the result is 3 and in the USA is 4 (everything is bigger in the USA, e.g. cars, etc.) :) Therefore I think "DIN 5477" is relevant here. To me, "3/4 of something" minus "2/4 of something" is "1/4 of something", but not "1 quarter point". Similarly, "44/100 of something" minus "40/100 of something" is "4/100 of something", but not "4 hundret points". The percentage is nothing, but a number (or ratio) expressed as a fraction of 100. So simple it is. If I see "44/100 of something" I can call it "44% of something". That's it. The same for "40/100 of something" and "4/100 of something". I'm not trying to remove percentage points from English. If anyone needs them, ok, no problem. But it is not the only option! And your own statements just proved it. (See your last two statements, which are synonymous according to you.) And that's exactly what the wiki doesn't reflect. The same for the increase. There is an actual increase, an absolute increase and a relative increase. If everything is "the increase", why should we distinguish between them? It must be short, but not accurate. Right? ToMiBi (talk) 09:44, 10 February 2021 (UTC)
- I do not know what "DIN 5477" means and do not have any idea why you think it is relevant here. This is the English wikipedia; in English, "A change of d percentage points" is completely unambiguous. Maybe in German this is not the case (I have no idea), or maybe DIN 5477 (whatever that is) is wrong. I don't see why that should be surprising. Certainly, I have seen instances of people trying to make changes based on ludicrous ideas like IEEE standards for how to write the number "e" are binding on wikipedia, and those always (and correctly) get repelled; the idea that we should follow standards from some non-Anglophone organization is even sillier. There is definitely a participant in this discussion in need of absorbing a new perspective, but I am afraid you have mis-identified who it is. --JBL (talk) 22:21, 9 February 2021 (UTC)
- Dear @JayBeeEll:, DIN 5477 standard (in german) explicitly recommends avoiding the term percentage point in order to avoid ambiguities and misunderstandings. Instead, the text or formula symbols should be used to clearly distinguish the difference between the ratios (relative changes) and the relative differences. So I think I have a significant group of people on my side with a different perspective. The true statement is that all uses of the words "percentage point" can be rephrased to not use those words! Actually, there is no real need for the term percentage point (from the mathematical point of view). The term percentage point is just a linguistic tool to express something briefly. It is very often used in economics. But economics is not the only discipline in the world. I just hope you don't claim that the DIN 5477 standard is wrong and everyone who doesn't use percentage points is confused. Please take a few minutes to look at this situation from this new perspective. Then you can go back to yours. Sincerely, ToMiBi (talk) 21:52, 9 February 2021 (UTC)
- Dear @JayBeeEll:, I really appreciate your reply. Thank you. OK then. Let's find the way to say that 1) if clearly defined, the p.p. is synonymous to the percentage (see your last two statements) and 2) everyone should be aware of what is being measured (see the definition on Wiki and your very first statement: 400% of what? If not spoken, it could be "... of the volume of the tank". To me, the change from "The water level has increased by 400%." to "The water level has relatively increased by 400%." makes a huge difference, since, the relative increase is expressed as a ratio, where the denominator represents an old value - and that defines the basis for the percentages.) May I ask you to clarify the definition on wiki, please? Maybe I am not the best person for that. But at least I can see that the current definition has flaws. ToMiBi (talk) 19:25, 9 February 2021 (UTC)
- Sorry, Bill, for dragging this out on your page. --JBL (talk) 11:58, 10 February 2021 (UTC)
- No problem Joel. There are some people who will not accept the obvious if it runs counter to their convictions (the U.S. Senate comes to mind here). I have given up on this individual and suggest that you might also. --Bill Cherowitzo (talk) 20:02, 10 February 2021 (UTC)
Why?
Sexism | |
I wonder why you have reverted several undid edits in the Fields Medal wiki page?! This is the first minutes of my activity on Wikipedia website on an account and I was just reading the Fields Medal page that came across an actual Sexism and wanted to edit that but I couldn't as I do not have a verified account. As a random visitor to the website, this is absolutely a case of sexism and it needs to be removed and maintained gender-neutrally. TraceyxD (talk) 01:44, 20 June 2021 (UTC) |