Hello everyone,
I was brought up to believe that the order of the factors is indifferent. That 9*7 equals 7*9. However, I've read a text in which the authors claims that there are systems in which this rule doesn't apply. Here's the text:
There are three basic properties of numbers, and you'll probably have just a little section on these properties, maybe at the beginning of the course, and then you'll probably never see them again (until the beginning of the next course). Covering these properties is a holdover from the "New Math" fiasco of the 1960s. While these properties will start to become relevant in matrix algebra and calculus (and become amazingly important in advanced math, a couple years after calculus), they really don't matter a whole lot now.
Why not? Because every math system you've ever worked with has obeyed these properties. You have never dealt with a system where a×b didn't equal b×a, for instance, or where (a×b)×c didn't equal a×(b×c). Which is why the properties probably seem somewhat pointless to you. Don't worry about their "relevance" for now; just make sure you can keep the properties straight so you can pass the next test. The lesson below explains how I kept track of the properties.
http://www.purplemath.com/modules/numbprop.htm
The authors doesn't expand any further on this. So i was wondering if anyone here would like to take the time out to educate me on this topic?
Thank you very much,
Nadeem.
I was brought up to believe that the order of the factors is indifferent. That 9*7 equals 7*9. However, I've read a text in which the authors claims that there are systems in which this rule doesn't apply. Here's the text:
There are three basic properties of numbers, and you'll probably have just a little section on these properties, maybe at the beginning of the course, and then you'll probably never see them again (until the beginning of the next course). Covering these properties is a holdover from the "New Math" fiasco of the 1960s. While these properties will start to become relevant in matrix algebra and calculus (and become amazingly important in advanced math, a couple years after calculus), they really don't matter a whole lot now.
Why not? Because every math system you've ever worked with has obeyed these properties. You have never dealt with a system where a×b didn't equal b×a, for instance, or where (a×b)×c didn't equal a×(b×c). Which is why the properties probably seem somewhat pointless to you. Don't worry about their "relevance" for now; just make sure you can keep the properties straight so you can pass the next test. The lesson below explains how I kept track of the properties.
http://www.purplemath.com/modules/numbprop.htm
The authors doesn't expand any further on this. So i was wondering if anyone here would like to take the time out to educate me on this topic?
Thank you very much,
Nadeem.
