In message Tue, 03 Jun 1997 17:25:59 -0400,
Sharon Smith <ssmith@ADMIN1.AUGUSTA.TEC.GA.US> writes:
> It has been a long time since I had theory of Algebra, but I seem to
> remember the Reals are a group under addition and as such needed '0' as
> the identity element. Am I remembering correctly?
>
>
>
>
> At 10:59 AM 6/3/97, you wrote:
>
>> You said "Thus 0 responds to the definition of element of the complex
>> set and ,
>> therefore it can be considered as a pure Imaginary number. "
>>
>> If 0 responds to the definition of element of the complex set (which I
>> agree with since I am thinking that 0 is Real and all Reals are
>> complex - the Reals are a subset of the Complex set) then how does it
>> follow that it is a pure Imaginary Number? Is the argument based on
>> your definition of a pure Imaginary Number? How are you defining a
>> pure Imaginary number?
>> Thanks,
>> Roberta
>>
>> At 09:16 AM 6/3/97, you wrote:
>>
>>>The 0 is Imaginary since 0i=i0=0 from its own property as the absorbant
>>> element for the multiplication in any subset of the complex set. And
>>> as the neutral element of the addition 0i + bi = (0+b)i = bi closure
>>> bi + 0i = (b+0)i = bi and if b=0 then bi=0i=0
>>> Thus 0 responds to the definition of element of the complex set and ,
>>> therefore it can be considered as a pure Imaginary number.
>>>
>>>
>>> At 07:10 AM 6/3/97, you wrote:
>>>
>>>>> What is the difference between a complex number, an imaginary number
>>>>> and a pure imaginary number. Somewhere I learned (but apparently in
>>>>> error) that a + bi is a complex number. If a = 0 then the
>>>>> number is imaginary. If b = 0 then it is a Real number.
>>>>>
>>>>>
>>>>>
>>>>
>>>> I learned basically the same thing. Every number is a complex
>>>> number and the complex numbers can be split into two categories, Real
>>>> and Imaginary (just as the Reals are either Rational or Irrational).
>>>> However, I don't buy the "0 is Imaginary" argument. It is on the
>>>> Complex Plane but it should be since the Reals are Complex.
>>>>
>>>> If I'm wrong, please set me straight since I teach this def. every
>>>> quarter!
>>>> Roberta
>>>>
>>>> ____________________________________________________________
>>>> Roberta S. Lacefield RSLace@mail.way.peachnet.edu
>>>> Waycross College http://members.tripod.com/~Roberta/index.html
>>>> 2001 S. Georgia Pkwy (912) 285 - 6027
>>>> Waycross, GA 31503 fax: (912) 287-4909
>>>>
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>>>
>>> "Thinking is the hardest work there is, which is the probable
>>> reason why so few people engage in it."
>>> Henry Ford
>>>
>>> Sounny Slitine
>>> epartment of Mathematics
>>>
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>>____________________________________________________________
>> Roberta S. Lacefield RSLace@mail.way.peachnet.edu
>> Waycross College http://members.tripod.com/~Roberta/index.html
>> 2001 S. Georgia Pkwy (912) 285 - 6027
>> Waycross, GA 31503 fax: (912) 287-4909
>>
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>>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Sharon Smith
> Augusta Technical Institute
> 3116 Deans Bridge Road
> Augusta, GA 30906
> Math Instructor
> Isa 43:1-3
> email ssmith@augusta.tec.ga.us
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
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Donna Whitfield
Dept. of Developmental Studies
Middle Georgia College
dwhitfie@warrior.MGC.Peachnet.EDU
The joy of the Lord is my strength
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