Talk:Empty product

message: We should say that 00 = 1 and it is an indeterminate form.  The two statements are both true.  Why would anyone have a problem with that? Michael Hardy (talk) 15:44, 17 June 2008 (UTC)
replies: text: Which article are you talking about, this one or exponentiation? You're right that it makes little difference whether an indeterminate form is "defined" or not. However, I just made a quick survey of three calculus texts from my shelf, and none of them defines 0^0 at all. Do you know of any calculus text that defines 0^0? — Carl (CBM · talk) 16:12, 17 June 2008 (UTC)

text: e^x = \sum_{n=0}^\infty {x^n \over n!}, 
since when x = 0 then the first term is 00/0!.  But why should it matter what calculus textbooks say about it?  Calculus texts are efforts at pedagogical improvements in ways to present standard material to students who don't want to become experts on it, not authoritative statements on issues on which there's no standard pronouncement. Michael Hardy (talk) 16:02, 18 June 2008 (UTC)

text: The exponentiation in the first term on the right-hand side is the real-to-integer, iterated-product version of exponentiation, not the real-to-real or complex-to-complex version, which as I say is intensionally quite distinct. But the point for WP purposes is that if there "is no standard pronouncement" then it's inappropriate for us to create one. --Trovatore (talk) 17:19, 18 June 2008 (UTC)

text: At this writing the article does not use the word convention, except when talking about the intersection of no subsets of a given set. --Trovatore (talk) 19:51, 18 June 2008 (UTC)
thread_title:  section break 2 

message: I've altered this section to read as follows:
: 
: Imagine a calculator that can only multiply.  It has an "ENTER" key and a "CLEAR" key. One would wish that, for example, if one presses "CLEAR", 7 "ENTER", 3 "ENTER", 4 "ENTER", then the display reads 84, because 7 × 3 × 4 = 84.  More precisely, we specify:
: 
:*A number is displayed just after "CLEAR" is pressed;
:*When a number is displayed and one enters another number, the product is displayed;
:*When "CLEAR" is pressed and then some numbers are entered, their product is displayed.
: 
: Then the starting value after pressing "CLEAR" has to be 1.  After one has pressed "clear" and done nothing else, the number of factors one has entered is zero.  Therefore the product of zero numbers is 1.
: 
Someone had changed it so that the third desideratum said that when clear is pressed and then a number is entered, that number is displayed.  In some ways that makes this closer to a logically rigorous argument, and in this context I think that in itself may be a mistake.  But also it doesn't seem so much like a self-evident desideratum since this whole thing is supposed to be about mutliplying. Michael Hardy (talk) 01:59, 12 October 2008 (UTC)
thread_title: Intuitive justification

message: I think this article is badly in need for rewriting to make more mathematical (and common language) sense. Take the opening phrase "an empty product, or nullary product, is the result of multiplying no numbers". No it is not, it is an expression asking for the product of an sequence (or set or multiset) of numbers (could be other things as well though), which sequence (set, etc.) happens to be empty. First, there is no such thing as multiplying no numbers, or even one or three numbers; multiplication takes two arguments (the distinction that should be made is between a multiplication and a product; possibly "multiplying together" can be used but it makes no good sense for 0 arguments). Second, and empty product is not the result of anything, it is something like "0!" whose value is 1, but it is not identical to 1 (or otherwise conversely "1 is an empty product", which seems a bad formulation). In short, one should make distinction between expressions and there values, and an empty product is an expression. But there are many more points that are just not carefully stated (and a lot non encyclopedic wording as well). I agree it takes effort to be clear and precise at the same time, but it is worth the effort. To get an idea look at empty sum, which I think is better. I plan to make changes here soon (but feel free to protest already). Marc van Leeuwen (talk) 08:15, 18 March 2010 (UTC)
replies: text: I cleaned it up a bit. There was too much repetition, and I deleted some things that were copied from other wiki-pages that were somewhat off topic.  MvH (talk) 00:19, 28 March 2014 (UTC)
thread_title:  Need for rewrite 

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thread_title:  External links modified