Talk:Value (mathematics)

Please help expand. Dullfig 19:07, 16 February 2006 (UTC)

'Values' as numbers

Should it be clarified that a value does not need to be a number? —Preceding unsigned comment added by 84.120.151.152 (talk) 14:46, 21 March 2008 (UTC)

'Values' as arguments

I am not happy about this stub. To say that 'functions map a set of values to another set of values' does not at all help the reader to understand the conventional distinction between function arguments (input) and function values (output). I strongly suspect that the person who formerly made a redirection to function had this distinction in mind. (By the way, this is the reason why real-valued function refers only to the range, not to the domain.) At the same time, I do recognise that we mathematicians tend to use the same terms in different meanings in different contexts; and 'values' of variables certainly are mentioned. In some common situations (e.g., with existing and non-zero Jacobians), you do not need to distinguish input from output very carefully; and the description supra might be more apt.

I would like to rewrite this in a more 'conventional' manner. Actually, I found the stub while looking for sensible references from an improved version of binary operation; but was disappointed.JoergenB 12:23, 15 September 2006 (UTC)

Go for it! Like I said above, the whole article is more of a "placeholder" than anything else. I am not qualified to write a math article, so why fake it? Dullfig 20:12, 15 September 2006 (UTC)

Headline text

What does vaule mean

-- I suppose it is a typo for value/poo :-) However, there are problems with this poo(supra).JoergenB 12:23, 15 September 2006 (UTC)

Value function

This would be a good place to introduce the concept of value function, which currently redirects to the Bellman equation page. Rinconsoleao (talk) 13:51, 27 September 2011 (UTC)

A value is a Canonical form

My understanding is that a value is a Canonical form of an expression that allows equality to be calculated by literally comparing the forms.

Is this right?

Thepigdog (talk) 09:20, 12 January 2014 (UTC)

No, a value is exactly what is said in the article and the notion of "canonical form" is not related to that of "value" (except that both notions may be applied to expressions. D.Lazard (talk) 10:11, 12 January 2014 (UTC)

Hmmm the previous stub said nothing other than a value is a value. But if you believe what I have written is completely wrong I will roll it back. It seems correct to me, but there may be some deeper mathematical truth that I am missing. I would appreciate any further comments you might make. I will do a little bit more investigation and roll it back in the morning if there is general consensus that I am barking up the wrong tree.

Under Canonical form it has,

"The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero."

This seems to absolutely agree with what I have written. Please explain what I am not understanding here.

I see that many fields associate a value with a number only, but this does not agree with common usage nowadays. We talk about the value of a Boolean, which has nothing to do with quantity. What then does evaluate mean?. Can I "evaluate" a Boolean expression, or evaluate a "set expression"? It seems to me that in common usage we can.

If we restrict the definition to numbers then a value is the canonical form of an arithmatic expression. Hmmm this does seem to be the dictionary meaning :(.

I would definitely say that the historical definition of a value is of quantity or worth, but that common usage, in all fields has evolved beyond that. However if there is agreement I am happy for my change to be rolled back. I cant think of another term I would use instead of value that would be used instead. Can I say "I evaluated the expression" only when the expression is for a number? What would I say instead? It is very limiting to restrict value to numerical value.

Thepigdog (talk) 10:43, 12 January 2014 (UTC)

This post and the edits you have done in the article appear to be your own original research. I recall you that original research is strictly forbidden in Wikipedia (see WP:No original research). As a consequence, I'll revert your edits in the article. However, if you find a reliable reference about this subject, I strongly invite you to improve the article accordingly. D.Lazard (talk) 12:44, 12 January 2014 (UTC)

Well I am certainly not trying to be original in any shape or form. To be honest it is blatantly not true that this is original research. The section on Canonical form says almost identically the same thing. I believe the changes are justified as unoriginal based on the Canonical Form article. Naturally I would love to have a reference, but for such a simple basic matter this may be hard to find. Please replace the changes for the moment in the hope that better mathematical minds can have a look at it, and either update it or add references. Thepigdog (talk) 13:03, 12 January 2014 (UTC)

Is there an expert we can push this too for resolution. Thepigdog (talk) 13:40, 12 January 2014 (UTC)

There is no need of an expert, because of WP:OR policy. Nevertheless, I am an expert. The following paragraphs are an answer to your previous post, written before reading your last post (edit conflict).

"Original research" has a meaning in Wikipedia that may be slightly different of the common usage. See WP:No original research for Wikipedia's definition. As the content of your edits does not come from your readings but is the result of your personal thought, it is blatant original research.

Moreover the first sentence of your edit is a mathematical nonsense. This sentence is "In mathematics, value is a Canonical form of a mathematical expression". Which significant "canonical form" does appear in the following sentence, which is not only mathematically correct but also similar with many sentences appearing in mathematical texts? "The value of x² + 1 is 5 when the variable x takes the value 2". D.Lazard (talk) 13:54, 12 January 2014 (UTC)

OK fair enough then. You clearly believe that what I have written is wrong. But the existing article says almost nothing about what a value is. You haven't answered the question "what is a value". You refer to a value twice in the one sentence without giving hint of what the purpose of a value is. Sigh. Anyway I give up. Sorry to trouble you. This is not personal at all and I have no problem with what you have done. Kind regards Thepigdog (talk) 14:09, 12 January 2014 (UTC)

Sorry I cant quite leave this alone. Which part of this is wrong.

• A natural number is represented by a sequence of digits. For example 122.
• 122 means $1*10^{2}+2*10^{1}+2$.
• 122 is a standard way of writing the number represented by the expression $55+67$
• 122 is a unique representation of $55+67$.
• Acording to Canonical form a canonical form is a
  • a standard form
  • a unique representation.
• So 122 is a canonical form.
• It even says in the article,
  • "The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero."

What part of this argument do you think is in any way wrong or original research? Doesn't it follow from this argument that a number is a canonical representation of an expression. By this I mean,

• 122 is a canonical form of $55+67$

My opening statement which you said was rubbish is,

"In mathematics, a value is a Canonical form of a mathematical expression."

So I am saying that 122 (clearly a value) is a canonical form of a mathematical expression (55+67). I am at a loss to see what your objection is. Please enlighten me. Would you have me find a reference to show that 55+67 = 122? Isn't basic maths and reasoning allowed? Thepigdog (talk) 15:50, 12 January 2014 (UTC)

unsourced information

WP:RELIABLE requires inline sources for all challenged material. NE Ent 15:25, 12 January 2014 (UTC)

The content that you have deleted is not challenged. If you think that some sentence is challenging, explain why in the talk page, and tag it with {{cn}}, but do not destroy relevant content. D.Lazard (talk) 15:32, 12 January 2014 (UTC)

I'm challenging it. Please provide sources. NE Ent 16:04, 12 January 2014 (UTC)

definition

The article as is doesn't define the meaning of "value".

"A value of a function is the result associated to a value of its argument "

Poor English at best. I presume you mean the,

"A function maps an argument to a value."

So suppose I have a function define by an equation,

f(x) = x + 5

Now f(7) should return the value of the expression 7 + 5. But we have not defined what a value is.

So we are defining a function as something that returns a value, and a value as that which a function returns. The argument is circular and tells us nothing about what a value is. This logic failure is there in the original Wolfram reference.

Thepigdog (talk) 17:28, 12 January 2014 (UTC)

Generally Wikipedia doesn't provide definitions per se -- that's Wiktionary's. The disambiguation page Value provides links to the corresponding wiktionary definitions. NE Ent 23:10, 12 January 2014 (UTC)

Do what you like

But remember the audience. The reader is important not you. If you are correct you have not explained yourself. And you have not answered the points above.

Hey its your page now, do as you will. Enjoy yourself. Kind regards Thepigdog (talk) 11:33, 13 January 2014 (UTC)

Added a reference

The book "Introduction to Modern Mathematics" describes a value as the output of a function. The input is the argument. That is very different from the modern understanding of a value in computer science. The meaning of the word seems to have morphed over time. To me "value" means some information (data) representing the state of something. The value is the representation, either as a series of bits, or digits or characters. If it is in a variable or is the output or input of a function is irrelevant. So these are values,

• 24 AUG 2009
• "a string"
• 3.141596
• 92
• $\lambda x.x$

However these have values but are not values,

• 46 * 2
• f(5)
• $(\lambda x.x)\ 5$

We may as well be being talking French and English. I can crawl back to the computer science realm, but I haven't found a mathematical definition of a computer science "value". I am expecting to see a definition,

$X=Y\iff \operatorname {value} [X]\equiv \operatorname {value} [Y]$

meaning that a value is a property of an expression which is the identical if the expressions are equal but not otherwise. The term "identical" means equal, in the domain of representations of values.

I am also expecting to see the following common axiom of mathematical systems.

$X\equiv X\implies X=X$

Meaning that two equivalent expressions must have the same value. Alternatively, every expression has one and only one value. How strange and confusing the terminology has become.

Thepigdog (talk) 02:51, 1 February 2014 (UTC)

Also

The phrase "also called the variable" is ambiguous. The value and the argument are both variable with most functions. — Preceding unsigned comment added by Montananevadagirl (talk • contribs) 12:31, 3 February 2014 (UTC)