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Topic: 2 simple? questions and proposed answers
Replies: 4   Last Post: Jan 29, 2012 7:50 AM

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Ed Wall

Posts: 845
Registered: 12/3/04
Re: 2 simple? questions and proposed answers
Posted: Jan 6, 2012 3:47 PM
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In a sense the business about 1 being a prime is a matter of convention (yes, it does make it easier to state some theorems). So, I would say people who are unaware of the messiness it would cause are probably right to be unimpressed.

As to multiplication of signed integers, I think saying the distribute rule has problems if not is, in fact, somewhat unconvincing (although, in a sense, what I say below is connected). Something a bit more convincing I've found (assuming people are comfortable with (a)(-b) = -(ab) [And this can be handled in a similar fashion] is simply something like

3 x -3 = -9
2 x -3 = -6
1 x -3 = -3
0 x -3 = 0
-1 x -3 = ?

Of course, mathematically the reason is that the integers are an extension of the counting numbers and hence your comment about the distributive law. The above just makes the structure a little more obvious.

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