Talk:Inequality (mathematics)/Archive 1

Archive 1

Names of the symbols ">" and "<"

Do the symbols ">" and "<" have names?

Greater-than and less-than, 'bra' and 'ket,' left and right 'brokets.'

Actually, "greater-than" and "less-than" are the most correct names. Brackets are somthing else, and they should be drawn thinner and taller than true inequality symbols. Melchoir 03:08, 3 November 2005 (UTC)

As mathematical operators, "greater-than" and "less-than" are the only correct terms; sometimes "sign" or "operator" is appended. When used for bracketing, they're often called "angle brackets". The "double angle brackets" symbols « and » that are used for French quotations and are properly called guillemets. See quotation mark#Angled quotation marks in various European languages for more. Deco 03:13, 3 November 2005 (UTC)

I want to stress that < and > should never be used as any kind of brackets, so if you ever have the occasion to call them brackets, then someone has already screwed up. In decent mathematical typesetting, these are the symbols used as, and called, angle brackets:

$\langle x\rangle$ End rant! Melchoir 03:27, 3 November 2005 (UTC)

P.S. ...except for email addresses.

...and HTML tags. :0) capitalist 03:58, 1 February 2006 (UTC)

see comment about somebody already screwing up. 128.135.133.72 19:53, 20 July 2006 (UTC)

The symbols are routinely used within Japanese script as a way to set off lower level headlines and so forth. For this reason, they're also routinely used by Japanese people for the same purpose within English (no matter how bizarre this looks to people who aren't Japanese). -- Hoary (talk) 00:25, 15 December 2012 (UTC)

Error

In the article is stated that: "For any real numbers, "a", "b", and "c": If c is negative and a > b; then a × abs(c) < b × abs(c) where abs(c) is the absolute value of c". But since abs(c) is positive..shouldnt a*abs(c) > b*abs(c) ? S Sepp 20:49, 18 January 2006 (UTC)

Yes, I've fixed it now. This whole section needs to be reformmated. Paul August ☎ 21:17, 18 January 2006 (UTC)

Alligator mnemomic

In the article the alligator mnemonic was mentioned as commonly used in the education of "less than" and "greater than". I have found this to be the rule rather than the exception throughout the United States. I believe its popularity should indeed be noted in this article, however, I also believe that its use should be curtailed if not eliminated due to the future confusion it sets up for students that learn it.

Daniel Patterson 18:44, 31 January 2006 (UTC)

I don't have statistics on how this is commonly taught, but I learned it in two ways. The first was to think of the inequality sign as an arrow, which always points to the lesser value (the value to the left on the real number line). The second way was to remember that the narrow part of the symbol always faces the lesser value, while the wide part of the symbol always faces the greater value. capitalist 04:01, 1 February 2006 (UTC)

Daniel Patterson, why does it set up 'future confusion'? Njál 19:13, 13 September 2006 (UTC)

The whole thing about the negatives just reaked of wikibikering so I deleted it. 128.135.133.72 19:51, 20 July 2006 (UTC)

feasible region

what the hell is that picture doing on this page? Feasible region isn't explained in this article, nor does it have a page on wikipedia. The picture therefore does nothing to aid this page. I would remove it.. but I would hope that instead someone can explain what it is. Fresheneesz 23:32, 8 March 2006 (UTC)

feasible regions are areas of the possible solutions to a system of inequalities. for that particular graph it was: x>0, y>0, and then is constrained by other lines. i'm going to crack open my algebra textbook and fix that. —Preceding unsigned comment added by 24.187.112.51 (talk) 03:27, 18 January 2008 (UTC)

need help

what do you call the type of notation for inequalities where x>5 is expressed [5,(infinity)]65.7.3.10 16:56, 10 August 2006 (UTC)

See Interval (mathematics). (By the way, use a ")", not "]", after the (infinity) symbol.) –dto 03:50, 1 September 2006 (UTC)

Confusing < and >

"Young students sometimes confuse the less-than and greater-than signs"

I'm curious: do dyslexic people have trouble with this as well? (More than 'older' students, who I think can still have as much trouble as young ones.) Njál 19:10, 13 September 2006 (UTC)

@Njal, We just hold up our left hand, and make an L, which means less than. —Preceding unsigned comment added by 149.152.34.41 (talk) 20:10, 15 November 2009 (UTC)

not <, not >

What are the modern symbols for 'not greater than' and 'not less than'? Njál 19:10, 13 September 2006 (UTC)

$\not >$ and $\not <$

really, is there any sense in making up these symbols? not greater than is just ≥, while not smaller than is simply ≥, so why make up any more of them?--Ghazer (talk) 22:10, 2 June 2008 (UTC)

Yes, it's called Partial Order.[[1]] —Preceding unsigned comment added by 69.231.207.125 (talk) 16:40, 19 February 2009 (UTC)

Power Inequalities

Can someone figure out what the subject and predicate of this first sentence are and explain what it's trying to say? It reads like grammatical gibberish at the moment, and without knowing it's point I can't fix it:

"Sometimes with notation "power inequality" understand inequalities which contain ab type expressions where a and b are real positive numbers or expressions of some variables."

Thanks. capitalist 02:34, 23 September 2006 (UTC)

Complex numbers

Complex numbers (with nonzero imaginary parts) are cannot be compared using inequalities. I think the article should explain this.

Tried to add the item, but couldn't get the format straight. Can some make it look a little bit prettier?

I've done a bit of that... The proof seems not quite right. "0 ≤ -1 which is false"? When did we say we were trying to define a total order that extends the order on the reals? I am sure a more general proof, of what was stated, is possible... Ordered field provides some useful properties, and states (without demonstrating) whether some fields can be ordered. Now, I think, it really must extend the order on the reals, because that is the only consistent ordering even in that subset of the complex numbers, but the proof doesn't currently show that. —Isaac Dupree^(talk) 13:14, 17 March 2007 (UTC)

I fixed it.--Patrick 16:20, 18 May 2007 (UTC)

Help

A friend wont believe me that 3 ≤ 5 is true because he believes both have to be true and i tell him that only one of then have to be true for the statement to be true. I found the example in my college algebra book and it says that 3≤5 is true but he believes that only X≤5 is true. Can anyone help me understand if I am wrong or help me explain if I am right? —The preceding unsigned comment was added by Barry White (talk • contribs) 05:31, 15 January 2007 (UTC). Barry White 05:33, 15 January 2007 (UTC)

It sounds like he doesn't understand what the ≤ symbol really represents. Does he read x ≤ 5 correctly, as "x is less than or equal to 5"? What this means is "x is less than 5 or x is equal to 5". This is a logical statement called an inclusive disjunction, made of two disjuncts:

• "x is less than 5"
• "x is equal to 5"

An inclusive disjunction is true when at least one of its disjuncts is true. So when we consider the case with 3 ≤ 5, the statement will be true if at least one of the two disjuncts, "3 is less than 5" and "3 is equal to 5", is true. Now clearly 3 is not equal to 5, so the second disjunct is false. But 3 is less than 5. So the first of the two disjuncts is true, and thus the whole statement is true. Maelin (Talk | Contribs) 10:26, 15 January 2007 (UTC)

Thank you

Im not saying that both have to be true at the same time im just saying that in order to use the symbol ≤ the number has to be both less in some circumstances and equal in others. Right? If not then wouldent using the sign here be wrong? If 3 is less then five then you would put < not , and ≤ and if 3 is equal to 5 you would put =. If I am wrong I dont understand why the symbols > and < exists if they can always be avoided by putting a line under them.

I thought the word or meant it had to be both in some case or you would just take it out all together. What I see him saying is 3<5 in some cases and 3=5 in other cases but what i've been taught is 3 doesn't equal 3.

Not quite. Basically what the mathematical statement x ≤ y means is, "x is not greater than y". It doesn't matter if they are never equal, or always equal (never strictly less); as long as x is not greater than y, the statement is true. Maelin (Talk | Contribs) 12:25, 16 January 2007 (UTC) ==

re: Applying a function to both sides

The section says that applying a strictly increasing (or decreasing) function to a non-strict inequality will make it strict. I think this is wrong. Because a non-strict inequality could mean they are equal; and thus after applying a function to both sides they could still be equal. --Spoon! 12:10, 11 March 2007 (UTC)

I just noticed this as well.

• 3 ≤ 3
• f(x) = x is a strictly increasing function. Let's apply it to both sides
• 3 < 3 (???)

Fixing the article ... —Isaac Dupree^(talk) 12:57, 17 March 2007 (UTC)

Inverse function

How do the inequality signs "behave" when the inverse function is applied?

For example, consider you want to identify all t for which the value of cos(t) < x₁. Keeping the definition domain for the principal value in mind, I'd say t > arccos(x₁)- notice the flipping inequality sign. Is this generally true when applying inverse functions? --Abdull 20:57, 18 June 2007 (UTC)

Internet Lingo: ">" -- it's almost like the new "owned!"

I've noticed on the Internet (forums, chat rooms, online gaming chats, etc.) that a lot of people, when they witness someone getting insulted or one-upped or proven wrong, say simply: "Winner>Loser", for example if Dave has just embarrassed, or totally destroyed an argument of, Mike, then a witness to this may simply type: "Dave>Mike" (usually followed by others saying simply "+1" in agreement etc.) I'm curious where on Wikipedia this kind of "casual 'Net lingo" should be located (if not already on here) and how the "Inequality" article could properly link to same. 199.214.28.241 22:42, 17 July 2007 (UTC)

Question on additive inverse

The property is shown as

The properties for the additive inverse state:

   * For any real numbers a and b
         o If a < b then -a > -b
         o If a > b then -a < -b

The question: Is this not actually a special case of multiplication where the factor c is -1? How is that an additive inverse?

Srobidoux 23:33, 9 September 2007 (UTC)srobidoux@verizon.net

If you're dealing with stuff like rings, there may be no "-1". So yes, it is a different property. Gscshoyru 01:25, 1 December 2007 (UTC)

What if c = 0?

In §2.5, I think we should add:

• If c = 0, then ab = ac. _{212.137.63.86 (talk) 12:59, 21 August 2008 (UTC)}

I believe you meant:   If $c=0$, then $ac=bc$,   right? Admiral Norton ^(talk) 13:06, 23 August 2008 (UTC)

Help on Representing Inequalities on the Real Number Line

I was actually looking here for help on my math hw, but couldn't find anything and instead found help by, searching on Google, at Wikibooks. Would this be of some use to the article? Or should we just cerate some sort of link. idk. Helixer (talk) 23:54, 13 September 2008 (UTC)

What about simply <x or >x?

I hope this makes sense, I'll do the best I can...

People often use of the symbol in writing or charts without a something on both ends, such as:

<x

rather than:

y<x

For example (the best I can think of now, though it is not ever used this way), the minimum height requirement to ride a roller-coaster might be written:

<3ft : allowed to ride

>3ft : not allowed to ride

I was actually trying to use this article to find out which way to face the symbol was correct:

<3ft : allowed to ride

or

>3ft : allowed to ride

We should add this to the article, maybe in a section on how the symbol is used in such a context (literature, charts, etc). Of course figuring out what is the correct use would be a first step.

NittyG (talk) 05:01, 17 March 2009 (UTC)

The second usage is correct. >3ft is read in English as "greater than 3 feet: allowed to ride", with the implication "forall p : People . h(p) > 3ft => p is allowed to ride". --207.173.201.99 (talk) 17:22, 5 May 2009 (UTC)

I think it's VERY important to include a simple basic definition of the primary meaning of the symbols as stated above. Many people come here seeking this definition since they see a number online, expressed as for instance >100 but have no clue which way to interpret or read that. More than, less than; larger than, smaller than. Because it also is used in terms of money and other things. This article should provide this simple primary meaning so people can get the basic meaning of the symbols. i came here to find it, and only found one reference to this usage here on the talk page because i know how to navigate wikipedia as a contributor. This small but significant part of the meaning and usage should definitely be on the page, near the top, in plain sight. First things first, and start at square one. Meat Eating Orchid (talk) 08:32, 14 July 2012 (UTC)

I second this question. At least, there could be a hatnote. -DePiep (talk) 10:44, 19 December 2014 (UTC)

Error in Representing inequalities on the real number line

The way this section is currently stated isn't clear, and is basically incorrect. It currently says:

"Every inequality (except those which involve imaginary numbers) can be represented on the real number line showing darkened regions on the line. A < or > is graphed by an open circle on the number. A ≤ or ≥ is graphed with a closed or black circle."

This is not true. If, for example, D : R -> R is the Dirichlet function (i.e. D(x) = 1 if x is rational, 0 otherwise) then the inequality D(x) > 0 can not be represented in such a method. In fact, the entire use of the term "represented" here is not really accurate. At the very least this section should be rewritten to make it clear that the inequality must be of the form f(x) > m for f a continuous function, or similar expressions replacing > with <, ≥, or ≤. (In fact, to be able to construct this type of diagram and display all the relevant information, we also need the condition that the regions in which f is not monotonic is bounded for x positive and for x negative, but this is somewhat irrelevant)

I will change it if no one responds to this, but my guess is that, given the level of the content, it is intended for elementary/middle schoolers and people who don't use mathematics often. As such, it would be better if someone who knows more about how to write properly for such an audience corrects it. 129.15.131.156 (talk) 06:10, 7 March 2010 (UTC)

Bad redirect

Difference (mathematics) redirects to this article. It should really redirect to subtraction. Could someone fix this?

129.96.220.98 (talk) 07:33, 23 February 2011 (UTC)

"≧" and "≦"

≧ also redirects, but is never addressed in this article. Is there a difference or are they the same symbols?--99.175.66.117 (talk) 00:07, 28 May 2011 (UTC)

Together with "≦" (which also redirects to the article), it is mentioned in the article, within the section "Vector inequalities". What isn't stated is:

1. how "≧" and "≦" are read (when used properly)
2. the fact (pointed out in this section of the Japanese version of this article) that "≧" and "≦" are in Japan merely the symbols used for what are elsewhere written as "≥" and "≤".

1. The relevant Unicode PDF calls the two symbols with the added horizontal "greater-than over equal to" and "less-than over equal to" respectively, unhelpfully refraining from indicating how they are used.

2. The relevant part of the ja:WP article is (like most of ja:WP) unburdened by any cited source. My own "OR" confirms that what it says is correct, but of course this isn't good enough.

-- Hoary (talk) 00:53, 15 December 2012 (UTC)

Part of the answer: see List of mathematical symbols, fifth and sixth items from the top of the table. Duoduoduo (talk) 13:00, 15 December 2012 (UTC)

Thank you! That's a lot more helpful than is the relevant part of this article. Should ≧ and ≦ redirect there rather than here? But no, it's (necessarily) a big, slowly loading page, within which particular symbols may be hard to find. Should the relevant material within it be copied from there to here? (Incidentally, its introduction seemed very woolly. I've revised it a little, though I realize that I am poorly qualified for the job.) -- Hoary (talk) 00:27, 16 December 2012 (UTC)

The redirect should definitely be to Inequality_(mathematics) (or maybe to Inequality_(mathematics)#Vector_inequalities), not to List of mathematical symbols. I'm trying to figure out what's deficient in the former compared to the latter. Remember also, that with symbols etc. that do not have widespread use such as these, it is probably best not to assume a firm definition or way of reading them: and encyclopedia should not set standards. Even the Unicode standard only gives a hint at what each symbol is for via a name and is not definitive. Something like this would have to be defined in any paper that uses it, and we do not have any references, which is problematic. Your edits to the symbols page are good: making the wording more precise is generally an improvement. — Quondum 07:41, 16 December 2012 (UTC)

Thank you. Emboldened by your kind words, I've made more changes just now. But the result isn't much good; it merely irritate me less than did its predecessors. Here's a quick link for editing the intro to this ponderous page. -- Hoary (talk) 23:19, 16 December 2012 (UTC)

Here are some references for the use of "≧" and "≦" in Japan.

• [2] an example for the Collaborative Reference Database by National Diet Library of Japan: How to read inequality symbols such as ＜ and ≦.
• [3] Sanseido Daijirin Japanese dictionary entry for 不等号 (inequality symbol) which shows not-greater-than and not-less-than symbols (等号付き不等号 lit. "inequality symbol with equality symbol") as a≦b and a≧b.
• [4] A research paper for high-school mathematical education by the National Institute for Educational Policy Research, an institute of MEXT. The paper uses ≦ and ≧ for quadratic inequation and range.

--Kusunose 14:08, 16 December 2012 (UTC)

Excellent work, Kusunose. I'm pushed for time right now, but later I'll look at your sources. -- Hoary (talk) 23:19, 16 December 2012 (UTC)

Chaining ≠ fails to specify relationship between non-adjacent items, or does it?

In the following statement:

a ≠ b≠ c

it is not expressly specified whether a can be equal to c, unless there is a convention. Is there a convention? I came across the problem in http://en.wikipedia.org/wiki/Lattice_type and couldn't find an answer on this page.

69.26.79.137 (talk) 22:53, 24 September 2012 (UTC)

I don't have a reference for this, but I've always interpreted it to mean two inequalities: a ≠ b and b≠ c, with no mention of whether a and c are equal. Duoduoduo (talk) 14:22, 15 December 2012 (UTC)

>=

If x >= 1, then

$x^{x^{x}}\geq x.\,$

should perhaps read

If x ≥ 1, then

$x^{x^{x}}\geq x.\,$

Bo Jacoby (talk) 21:07, 18 December 2012 (UTC).

Fixed. ">=" is an inappropriate symbol in this context. — Quondum 05:41, 19 December 2012 (UTC)

Other symbols of inequality

There are other symbols of inequality used in mathematics that could be added to the article.

≮ not less-than

≯ not greater-than

≰ not less-than or equal to

≱ not greater-than or equal to

≨ less-than but not equal to

≩ greater-than but not equal to

≅ approximately equal to

≆ approximately but not actually equal to

≇ neither approximately nor actually equal to

≈ almost equal to

≉ not almost equal to

≊ almost equal or equal to

≍ equivalent to

≭ not equivalent to

≲ less-than or equivalent to

≳ greater-than or equivalent to

≴ neither less-than nor equivalent to

≵ neither greater-than nor equivalent to

≘ corresponds to

≙ estimates

≡ identical to

≢ not identical to

≣ strictly equal or identical to

Sg647112c (talk) 20:22, 7 August 2014 (UTC)

"sharp" inequality

An inequality is "sharp" if there is no tighter inequality relating the two sides. I looked for articles that might define the term, but I couldn't find any on WP. I s'pose it doesn't deserve an article all its own, but the definition belongs somewhere, right? cheers, 24.240.67.157 (talk) 00:11, 5 July 2015 (UTC)

For example, the triangle inequality is sharp as is the Cauchy–Schwarz inequality. 24.240.67.157 (talk) 00:14, 5 July 2015 (UTC)

Finnish

Epäyhtälö does NOT mean inequality but inequation, fixed and the link removed from this page. 188.238.47.255 (talk) 11:04, 29 February 2016 (UTC)

Edit: I suggest you check if this is also done incorrectly in other languages. 188.238.47.255 (talk) 11:07, 29 February 2016 (UTC)

What do ⋖ and ⋗ mean?

The two characters ⋖ and ⋗ redirect here, but they don't occur in the article. Can someone please explain them? (BTW, those redirects were created by a user who apparently mass created such redirects for characters without caring if the target said anything about them; see e.g. Wikipedia:Redirects for discussion/Log/2013 October 7#⎶.) — Sebastian 09:39, 15 March 2018 (UTC)

Within the Unicode standard these characters are U+22D6 ⋖ LESS-THAN WITH DOT and U+22D7 ⋗ GREATER-THAN WITH DOT, see Mathematical Operators or "Mathematical Operators". The corresponding HTML5 entities are &gtdot; and &ltdot;. I don't know how these characters are commonly used, sorry. (And I actually have not seen them used at all in the books on order theory I know.) – Tea2min (talk) 10:04, 15 March 2018 (UTC)

There's a template for redirects without a mention of the target term: "R without mention". ZFT (talk) 03:47, 21 July 2020 (UTC)

Generally, "what does symbol ... mean?" is not a good question, because since Hilbert's famous saying (David_Hilbert#Axiomatization of geometry) mathematics is independent of notation. To find out what a symbol means in some publication, you should read its definition section. That said, I've seen "⋖" denoting the irreflexive kernel of term subsumption by Dershowitz and Jouannaud (1990) (p.250) and of substitution subsumption (p.251). However, I bet, there are other authors who use that symbol in a completely different way. - Jochen Burghardt (talk) 09:10, 21 July 2020 (UTC)

References

As they are clearly mathematical symbols, but we do not know any notable use of them, I have redirected both to List of mathematical symbols#Symbols that point left or right, where these symbols do not appear either, but which contains the symbol <·. So, the new target is less confusing. D.Lazard (talk) 13:52, 21 July 2020 (UTC)

Merger proposal (Inequation)

I propose the merging of Inequation into Inequality (mathematics); "inequation" is a less common term for the same thing, making it effectively a duplicate-topic article, and the inequation article is significantly shorter. Xnft (talk) 21:14, 14 March 2021 (UTC)

Correction: "less common term for the same thing" is an exaggeration. Inequality and inequation are not exactly the same thing, but they are closely related topics, so I'm maintaining the proposal. Xnft (talk) 21:18, 14 March 2021 (UTC)

• Oppose. The topics are different. "Inequality" is about > while inequation is about ≠. Instead, Inequation should be rewritten for focusing on its subject. Note that in the reals the concepts are close together, as ≠ is the conjonction of < and >. However, this is not true in the complexes, where "inequality" is nonsensical. D.Lazard (talk) 10:13, 15 March 2021 (UTC)

⋘

⋘ redirects here, but it is not mentioned at all. Is that O.K.?--Backinstadiums (talk) 09:53, 8 April 2021 (UTC)

It is OK that this uncommon symbol is not mentioned here. I changed the target of this redirect (and 7 similar ones) to Mathematical Operators (Unicode block). D.Lazard (talk) 11:08, 8 April 2021 (UTC)

U+2A85 ⪅ LESS-THAN OR APPROXIMATE

Just wondering why not cover this well-defined operator here. fgnievinski (talk) 15:16, 18 November 2021 (UTC)

This is a well defined typographical symbol, not a well defined mathematical operator. Unicode being not a mathematical authority, the name that that it gives to a symbol has no mathematical relevance. For mentioning a symbol in a mathematical article, a mathematically reliable source is required. Should I recall that this is a mathematical article? D.Lazard (talk) 15:48, 18 November 2021 (UTC)

The article already covers some abuse of notation, such as "In engineering sciences, less formal use of the notation is..." — for consistency, you should remove that and redirect Much-less-than sign as well. I acknowledge not all related Unicode operators are as well defined, but U+2A85 ⪅ clearly is. fgnievinski (talk) 16:46, 18 November 2021 (UTC)

The mathematical use of a notation is worth to be mentioned in a mathematical article, even if its use is common only in applications outside mathematics. Unicode symbols are not mathematical use.

Moreover, MOS:MATH recommend to not use in Wikipedia a uncommon Unicode symbol that is not well rendered in every font on every browser. This is the case for ⪅, at least on a standard Safari browser. Such a symbol should be displayed with LaTeX. Unfortunately this is a macro that does not exist in WP LaTeX (this shows that these symbols are very uncommon in mathematics). D.Lazard (talk) 17:46, 18 November 2021 (UTC)

I agree with D.Lazard that "⪅" is not a mathematically well-defined operator, and hence should not be included here. What is more, I think fgnievinski has a point in that "≪" is not well-defined, either, and should be removed here, too. I hardly can think of any mathematical reasoning involving "⪅" or "≪", they both are just pseudo-formal notation for sloppy informal statements. - Jochen Burghardt (talk) 20:06, 18 November 2021 (UTC)

Jochen Burghardt Sure, I've split all the approximate inequality operators. D.Lazard you're wrong about Latex. fgnievinski (talk) 23:08, 19 November 2021 (UTC)

@Fgnievinski: Your creation was somewhat hasty; merging the stuff into Approximation#Mathematics would have been an alternative that I'd liked to discuss before. - As another point, if any mathematical properties about "≪" (I guess, it is always a strict partial order) or "⪅" (I guess it is always a quasitransitive relation) can be stated, this should be done in the new article. Similarly, if any precise definitions are around (I could imagine e.g. x≪y if x<y*0.001, and x⪅y if x<y+0.001), they should be given there, too; they may vary with the author, such that several citations would be needed. - Jochen Burghardt (talk) 17:39, 20 November 2021 (UTC)

Jochen Burghardt The definition can be stated via logical AND as x≪y: (x<y) ∧ (x≇y), where the latter is U+2247 ≇ NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO. fgnievinski (talk) 01:33, 22 November 2021 (UTC)

Then, what is the definition of x≇y, and what properties can be stated about this relation? - Jochen Burghardt (talk) 09:42, 22 November 2021 (UTC)

x≇y: |x-y|<ε, where the tolerance ε depends on the context. fgnievinski (talk) 17:56, 22 November 2021 (UTC)

You probably mean the negation, that is, x≇y: |x-y|≥ε? Anyway, if ε is small (as it usually is), your above definition of x≪y is incompatible with its common use. - Jochen Burghardt (talk) 19:30, 22 November 2021 (UTC)

It seems the discussion has moved elsewhere. fgnievinski (talk) 03:45, 24 November 2021 (UTC)

"Ungleichung" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Ungleichung and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 13#Ungleichung until a consensus is reached, and readers of this page are welcome to contribute to the discussion. ~~~~
User:1234qwer1234qwer4 (talk) 02:41, 13 February 2022 (UTC)

Renderization of "not greater than" symbol

In my computer, the LaTeX alternative is the only one in which the slash overlays the angle bracket:

• Poor-man's: 1≯ 2
• Unicode: 1≯2
• HTML: 1≯2
• LaTex: $a\ngtr b$

Edit: my cellphone renders the symbol better:

Edit 2: I've filled a bug report. fgnievinski (talk) 19:06, 9 April 2024 (UTC)

Also:

• Poor-man's + {{math}}: 1≯ 2
• Unicode + {{math}}: 1≯2
• HTML + {{math}}: 1≯2

This is one of the reasons for which it is recommended to render the special symbols in latex only. By the way, Beland makes a great job in implementing this recommendation in many articles. D.Lazard (talk) 20:03, 9 April 2024 (UTC)

@Fgnievinski: When I reverted your recent edit, I wasn't aware of this discussion - please apologize.

My intention was (and is) to avoid repetition in the text. If there is one version (LaTeX?) that is rendered satisfactorily on all systems, I'd suggest to use just this version until the bug is fixed. - Jochen Burghardt (talk) 08:53, 10 April 2024 (UTC)

@Fgnievinski: It looks like the first three techniques are all the same, just using the Unicode character U+226F in one way or another. Before I ask for consensus for a general rule to fix this, do the {{math}} versions render correctly for you? Are there any other related characters that render incorrectly? -- Beland (talk) 01:46, 12 April 2024 (UTC)

@Beland {{math}} doesn't improve the results in Chrome, unfortunately. Thanks for looking into this. I'm puzzled why folks at Phabricator don't think this is a bug. fgnievinski (talk) 13:20, 12 April 2024 (UTC)

Because it's at the Operating System level. It's a bug, just not one we can deal with. Please contact Microsoft. —TheDJ (talk • contribs) 09:29, 15 April 2024 (UTC)

But it works with Firefox, with the same O.S. So, should one contact Google, instead? The Web is supposed to be interoperable. It's hard not to agree with fellow editors who propose giving preference to LaTeX in Wikipedia. fgnievinski (talk) 02:10, 16 April 2024 (UTC)

Started discussion at Wikipedia talk:Manual of Style/Mathematics#Not-greater-than rendering problems. -- Beland (talk) 02:39, 18 April 2024 (UTC)