Talk:Expression (mathematics)

message: Should this be moved to algebraic expression? Septentrionalis 15:42, 20 September 2005 (UTC)
replies: text: 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)
replies: text: Yes, but they're not really discussed in this article. Septentrionalis 16:58, 24 September 2005 (UTC)

text: I'm not sure about your article algebraic expression.  According to your usage, expressions involving pi and e are not algebraic expressions because pi and e are not algebraic numbers.  That's not a usage I've ever heard.  Rick Norwood (talk) 17:41, 28 October 2011 (UTC)
replies: text: It's a very good point you make. The sources I found indicate that expressions involving transcendental numbers are not considered as algebraic expressions. It's at least consistent since the algebraic numbers form a field, the algebraic closure of the rational numbers. It also fits to the informal definition in the lead of the article algebraic function. Actually, the reason I've been considering this is that I wanted to define what an algebraic fraction is—another article I've created. The background was that I wanted to find out whether all examples in the article Fraction (mathematics) should really be called fractions. The results would indicate that e.g. √2/2 and \frac{2+i}{2-2 \cdot i} are rational algebraic fractions since they involve only algebraic numbers, whereas π/4 is not, since π is transcendental. Do you know of sources claiming otherwise? Isheden (talk) 21:59, 28 October 2011 (UTC)
thread_title: Algebraic expression

message: 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)
thread_title:  explicit vs implicit expression 

message: "... is not [an expression], because the parentheses are not balanced and division by zero is undefined."  Does that make sense?  That x / 0 is not mathematical expression just because it's undefined? Saeed Jahed (talk) 10:19, 15 March 2009 (UTC)
replies: text: A nonsense string of symbols is not considered a (well formed) mathematical expression.  As another example "3 @ 4" would not be considered a mathematical expression because the operation "@" is undefined.  On the other hand, if a definition of "@" were given in the preceding text, then "3 @ 4" would become a mathematical expression.  There is a large body of literature on what constitutes a "well-formed formula".  Rick Norwood (talk) 14:45, 15 March 2009 (UTC)

text: Not sure if what Rick said is relevant. Certainly the unbalanced parens discount it from being an expression. However, division by zero (x / 0) is certainly a perfectly valid expression -- its value is undefined, but it is an expression. Therefore, I have changed the counter-example to ")x)/y", and removed the statement about division by zero. (There is even a later example of an expression being undefined due to division by zero). EatMyShortz (talk) 07:22, 31 August 2009 (UTC)
replies: text:  Support: Division by 0 is, correctly, undefined. However, "(x ÷ 0)" is correct when defined as a mathematical expression (which has been defined in Expression_(math).) ACredibleLie (talk) 15:15, 18 February 2010 (UTC)
thread_title:  Division by zero not an expression? 

message: I agree that this article (and all other articles on elementry mathematics) must be as easy for a non-mathematician to read as possible.  I've shorted and simplified the first paragraph.  
As best can see, the second paragraph, beginning "In algebra..." does not say anything that needs to be said here.  Do I hear any objection to removing it?
On the other hand, we might want to add a little bit about the rules for well-formed formulas.
Rick Norwood (talk) 17:59, 28 October 2011 (UTC)
replies: text: I think the paragraph you mention can be removed. Possibly algebraic expression could be merged into this article instead. Isheden (talk) 22:02, 28 October 2011 (UTC)
thread_title:  Isheden's complaint 

message: This pearl of prose is hardly encyclopedic language. It should be rephrased. FilipeS (talk) 18:55, 5 April 2012 (UTC)
replies: text: Agree. Possibly algebraic expression could be merged into this article if it becomes more encyclopedic. Isheden (talk) 08:12, 6 April 2012 (UTC)
thread_title:  "Meaningless jumble" 

message: In the section Different forms of mathematical expressions,  the table says that arithmetic expressions can have factorials but not integer exponents. This seems contradictory: each is simply a sequence of multiplications, in one case like 4×3×2×1, and in the other case like 4×4×4×4. So they both ought to be allowed or not allowed.
Also, since the table says that polynomials can contain an "integer exponent",  I think that row heading should be renamed "Positive integer exponent" or "Non-negative integer exponent".Loraof (talk) 20:25, 29 September 2014 (UTC)
replies: text: Good points. Another problem with the table is that it says polynomials can have elementary arithmetic operations, but polynomials do not have division. BTW, the table is a template: Template:Mathematical expressions. --50.53.46.203 (talk) 14:29, 1 October 2014 (UTC)
thread_title:  Inconsistency in table 

message: There is no section describing how and when symbolic expressions were developed and replaced text.  FreeFlow99 (talk) 09:49, 6 November 2015 (UTC)
replies: text: The problem for that is the lack of WP:Reliable sources. In fact, as far as I know, there are two periods. The first one is the introduction of mathematical notation, which is described in History of mathematical notation. However, the concept of "expression" appeared much more recently. I suspect that it has been rarely used before the second half of the 20th century, when it has been popularized by its use in computer algebra and other aspects of the computerization of mathematics. In fact, that is the computerization that requires a clear distinction between a mathematical object and its various representations as expressions. Moreover, in relation with computer proofs, a formal definition of "expression" is often needed, and there is not yet a general agreement of what should be such a formal definition. This explains the lack of reliable sources for the history of the notion. D.Lazard (talk) 15:18, 6 November 2015 (UTC)
thread_title: No History