Talk:Inequality

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

Insertformulahere

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)

Contents

[edit] 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)


[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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) ==

[edit] 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.

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

[edit] 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)

[edit] 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)

[edit] 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)