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Topic: [ap-calculus] Number System
Replies: 1   Last Post: Oct 17, 2012 2:03 PM

 Jeff Stuart Posts: 1,086 Registered: 12/6/04
Re: [ap-calculus] Number System
Posted: Oct 17, 2012 2:03 PM

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Debbie:

In some sense, neither and both are correct.

The real numbers PARTITION into two sets of numbers: rationals and
irrationals.
The real numbers also partition into the algebraic and the transcendental.
The real numbers also partition into the negative and the nonnegative.
We partition the real numbers into different (disjoint) subsets
depending on what properties are of interest.

Meanwhile, and independently, we can partition the complex numbers into
various disjoint subsets.
The algebraic and the transcendental.
Those with negative imaginary part and those with nonnegative imaginary
part.
Those with positive imaginary part and those with nonpositive imaginary
part.
Those with positive imaginary part, those with negative imaginary part,
and the real numbers.
The real numbers, the nonzero imaginary numbers, and the complex numbers
with both nonzero real and nonzero imaginary parts.
The real numbers can be represented as all complex numbers a + 0i where
a is real.
The imaginary numbers can be represented as all complex numbers 0 +
bi where b is real.
The imaginary and real numbers intersect at the origin 0 = 0 + 0i.
Properly speaking (and writing), a number such as 3 + 4i is a
"nonreal complex number". It is neither real nor imaginary.

Jeff

On 10/17/2012 10:24 AM, Debbie Bricker wrote:
> NOTE:
> This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus
> Teacher Community Forum at https://apcommunity.collegeboard.org/getting-started
> and post messages there.
> ------------------------------------------------------------------------------------------------
> We are having this discussion among our department....which is correct?
> 1) Number System having two subsets: Real(rational and irrational) and Imaginary(which includes complex numbers) OR
>
> 2) Complex Number System having two subsets: Real and Imaginary
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>

--
Professor Jeff Stuart, Chair
Department of Mathematics
Pacific Lutheran University
Tacoma, WA 98447 USA
(253) 535 - 7403
jeffrey.stuart@plu.edu

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