Posted by T.Gracken on October 18, 2002 at 18:00:12:
In Reply to: Re: about the commutative properety of multiplication posted by MathBard on October 18, 2002 at 11:58:15:
I didn't mean to imply you were arguing. I also didn't mean to imply you did not understand the 'commutative property of multiplication'.
What I meant to write was simply "the commutative property of multiplication IS the justification for disregarding the order of factors.
Not everyone does realize 3 times x is the same as x times 3 when using symbols. Also, until a person learns certain multiplication tables, it is not inherently obvious that 4*6 = 6*4.
So I was really just trying state, the commutative propery means (in English) that if one is multiplying two numbers, the order doesn't matter.
As far as proper... 8x and x8 are both proper because of the commutative property. It is just prefered by most to write the constant first (that is, to the left) and that's why we need justification.
So, I am sorry... I didn't mean to "sound" as if I were attacking you, arguing, or attempting to soil your credibility, and I apologize if that was how you read it. I have poor English skills (that's one reason why I am a math nerd) so I tend to speak/write before I think.
It is difficult (at least for me) to interpret written words and the attitude they were written under...
...except for Mr.B. whose math can be taken seriously, but whose comments must always be considered lighthearted and friendly (yet still serious).