Talk:Expression (mathematics)

From Wikipedia, the free encyclopedia

WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Stub Class Mid Priority  Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article.

[edit] Algebraic expression

Should this be moved to algebraic expression? Septentrionalis 15:42, 20 September 2005 (UTC)

I think not. There are many expressions such as \int_0^t f(x) \,dx which are usually not called "algebraic". --Aleph4 16:03, 20 September 2005 (UTC)
Yes, but they're not really discussed in this article. Septentrionalis 16:58, 24 September 2005 (UTC)

i think we are all missing the point. by our clumsy definitions of the basic algebraical terms and making them too technical the essence of mathematics is being taken away from the masses. it is high time we make proper changes. i request all to refer to hall and knight's elementary algebra for schools and then build up from there.

Should the link to axiomatic theory of expressions be removed? It's a poorly organized page that describes some guy's new "theory" about the foundations of mathematics. He's still developing his theory. I don't have the knowledge to adequately evaluate his claims, but it looked pretty sketchy to the untrained eye. I expect the link was added by the fellow himself.

[edit] Numbers or numerals?

Oleg just reverted this, but I think the proper term is "numerals". An expression is a combination of symbols. A number is not a symbol, but a numeral is. Therefore, expressions contain numerals; they do not contain numbers. Other thoughts? I'll re-revert if there are no objections in the next day or so. capitalist 02:53, 14 June 2006 (UTC)

Why do you say that a mathematical expression is a combination of symbols? Do you have a reference for this? I think it is a combination of numbers, not numerals, together with functions and variables (see my comment on Talk:Complex number). -- Jitse Niesen (talk) 05:17, 14 June 2006 (UTC)
Yes, the reference is the Merriam Webster's Online Dictionary which gives this definition:
1 a : an act, process, or instance of representing in a medium (as words) : UTTERANCE <freedom of expression> b (1) : something that manifests, embodies, or symbolizes something else <this gift is an expression of my admiration for you> (2) : a significant word or phrase (3) : a mathematical or logical symbol or a meaningful combination of symbols (4) : the detectable effect of a gene; also : EXPRESSIVITY 1
So given that definition, we can conclude that a mathematical expression is a group of symbols. Given that conclusion and the fact that numerals are symbols while numbers are not, we can conclude that mathematical expressions contain numerals, not numbers. QED! :0) capitalist 03:28, 15 June 2006 (UTC)
The Oxford English Dictionary has a similar definition—unfortunately there is no Mathworld article on it. However, with the example given at Talk:Complex number of Polish notation of "+ 1 1" being the same expression, with just a different notation, as the common infix "1 + 1", I do not know that this is sufficient. This has the same numbers operated on by the same operator; and both mean what is possibly another notation "one plus one". Is this different because the symbols are different, where the Polish notation has the same symbols in a different order? Still, certainly, a expression is still a representation, and "3 - 1" is not the same expression as "1 + 1". —Centrxtalk 07:14, 15 June 2006 (UTC)

It is possible to be right and wrong at the same time. Yes, there is a distinction to be made between numbers and numerals and, yes, an expression contains the latter, not the former. However, it is equally true that 2 plus 2 is not 4. Rather, we should say that the number represented by the numeral 2 added to the number represented by the numeral 2 yields the number represented by the numeral four. That sort of excessive precission is called pedantry, and is to be avoided. Make the technical distinctions only in cases where they matter. Rick Norwood 15:34, 15 June 2006 (UTC)

No, when a word is used in language, the meaning to which it refers is always implied, that is the prime and default purpose of language. When a term is used as term, it is the exception and has special formatting to indicate it, in such examples as — Depend derives from the same word as pendulum. — and — The word "cat" designates a feline. — but that does not mean that it is false to say that "A cat is a feline." It is the reason why on Wikipedia each article begins with something like "The United States is a country" rather than "The United States is the name of a country". The fact remains that we are defining what an expression is. If an expression is, in fact, a combination of numerals,etc. rather than numbers, then defining it as number would be equivalent to saying "The United States is a continent" or the "United States is a population", not the pedantry of defining it as as term. —Centrxtalk 19:20, 15 June 2006 (UTC)

You are splitting hairs. If I did the same, I could object that "The United States" is not the name of a country. The name of the country is "The United States of America". Rick Norwood 21:09, 15 June 2006 (UTC)

You are incorrect. If an expression does not consist of numbers, then defining it as such would be false. The analogue would be stating that the name of the United States is "Northern Hemisphere". If indeed, this were simply splitting hairs, then it should be perfectly acceptable to you either way. —Centrxtalk 21:35, 15 June 2006 (UTC)

[edit] explicit vs implicit expression

In Golden_ratio, there is a redlink to "explicit expression". Is this a well defined math concept? If so, it might be useful to define it in this article? — Xiutwel ♫☺♥♪ (talk) 21:08, 22 December 2007 (UTC)