Talk:Multiplication
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Old article:
For every assortment (unique or otherwise) of numbers there is a unique number called the product. Any two numbers in such an assortment can be replaced with their product without effecting any change in the product of the assortment. Any number of ones can be added or removed with no change in the product. Assortments with products other than zero contain only numbers other than zero.
The word multiplication also is used to refer to reproduction.
"Any two numbers in such an assortment can be replaced with their product without effecting any change in the product of the assortment."
This isn't a property of multiplication. This is a property of algebra that states for B = A, B can be substituted for A in any expression without effecting the value of the expression.
The note on reproduction should probably be re-added, though.--BlackGriffen
No, no, you're both missing the point of the original article (which is not mine, but I know enough about group theory to understand it). The text above describes the meaning of "multiplication" in group theory, which is any operation (such as traditional multiplication, which the article now describes) that has the properties noted. The specific property mentioned above is not simple one-for-one substitution. Read it again: it's two-for-one substitution. For any collection of numbers, any two can be removed and replaced by the one number which is the product of those two numbers, and the product of the collection will stay the same. --LDC
Would it be too much trouble to motivate how multiplication gets defined for the rationals and reals? Also, the first paragraph is problematic in defining multiplication as repeated addition; how do you add 2.5 to itself 3.7 times? --Ryguasu 01:56 Feb 25, 2003 (UTC)
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[edit] error... :S
I think there is an error, when defining the infinite products from -oo to +oo as the sum of two limits, instead of the product.
Marçal
[edit] Multiplication for non-integers
Could anyone write about how to define multiplication for non-integers in the article? (Current, it says one can define multiplication for real numbers but does not say how.) Or more like is it impossible? -- Taku 18:45, Apr 2, 2005 (UTC)
- I will try to do so, or at least put an adequate link.
- The idea is that rationals are obtained from integers by localization, and reals are obtained from rationals as factor ring, idem for complex numbers from reals. Both operations involve an injective ring morphism, so that the result of multiplication remains the same for elements of the previous subset. MFH 17:42, 5 Apr 2005 (UTC)
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- In other words, one first defines the multiplication of integers, then the multiplication of rationals in the usual way, by multiplying the numerators in denominators. After that, if one wants to multiply to real numbers, one approximates them by rationals and multiplies the rationals instead. Of course, to make this rigurous, you create two sequences of rational numbers converging to the two real numbers, then the product of that pair of rationals converges to the product of the pair of reals.
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- I could go in more detail if necessary. Oleg Alexandrov 17:58, 5 Apr 2005 (UTC)
- There is another way to address multiplication for the rationals which doesn't require localization. Define non-zero rationals to be pairs of non-zero integers and with the multiplication induced from Z(+)Z quotient the set by the equivalence relation (a,b)~(c,d) iff ad = bc. If you want a more algebraic sort of quotient, you can describe the multiplicative structure of Z\{0}(+)Z\{0} as a semigroup.
- As for the reals in my opinion the best way to characterize them is as the fraction field of power series in one variable with coefficients in Z/pZ quotiented by (x-1/p). As we exploit the fraction field construction, we might as well use localization in defining the rationals. TJSwaine 12:10 3/24/2006
[edit] Add m to itself n times
I think in the Discussion section "Add m to itself n times" should actually read "Add m to itself n-1 times". Adding m to itself once is m+m. --Heycam 08:45, 9 Apr 2005 (UTC)
In my opinion n x m, which reads as n times m, should be interpreted as m+m+...+m, rather than n+n+...+n. I can imagine laying 5 times a pound on a table, but hardly laying a pound times 5. 130.89.220.52 21:19, 16 Apr 2005 (UTC)
[edit] Multiplication tricks
There are many tricks out there, we've all seen those mofo's who use their fingers to multiply things like primative abacii and envied them terribly. I recently learnt the trick to the nine times table one, there are many more; further there are many simplistic methods of dealing with even large number multiplication. If I were to do a summary of the nine times in a seperate article and link it through to here, would anyone else be willing to take on the challenge of equalising for all the geeky kids out there who went through the same mathmatically repressed childhoods that us non-finger-jedi-masters went through with me? :P Jachin 12:23, 11 May 2006 (UTC)
[edit] Quaternions
In the section on properties, should it be mentioned that commutativity doesn't hold over 
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- I'm not sure either way. This article's scope isn't terribly clear to me. Noncommutativity is mentioned at Product (mathematics), at least. Melchoir 18:37, 29 June 2006 (UTC)
- Never mind, I'm stupid; ArnoldReinhold already worked it in! Melchoir 18:41, 29 June 2006 (UTC)
[edit] Correction to Multiplying Fractions example
I made a change to the example of multiplying fractions in the introduction. It used to say "a/b × c/d = ac/bd" and I changes it to "a/b × c/d = (ac)/(bd)" meshach
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- Definitely the parentheses in the denominator should be there to avoid what would be ambiguity at best. Michael Hardy 00:42, 3 July 2006 (UTC)
