Assignment 1 : Problem 2

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Aaron Albers

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Sep 14, 2010, 11:05:36 PM9/14/10
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For n \in \!\, \mathbb{Z} \!\,, let An = {a \in \!\, \mathbb{Z} \!\, | a <= n }

(b) A3 \cap \!\, A-3
(c) A3 \cap \!\, (A-3)^c
(d) \cap \!\,^4 Ai

Aaron Albers

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Sep 14, 2010, 11:07:47 PM9/14/10
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(b) A3 \cap \!\, A-3
This would go from -3 to 3

 A3 \cap \!\, A-3 = {-3, -2 -1, 0, 1, 2, 3}

Aaron Albers

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Sep 14, 2010, 11:28:58 PM9/14/10
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I take it back.

The only intersection that A3 \cap \!\, A-3 has is -3 to -infinity

A3 \cap \!\, A-3 = {a \in \!\, \mathbb{Z} \!\, | a <= -3 }

Aaron Albers

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Sep 14, 2010, 11:31:06 PM9/14/10
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(d) \cap \!\,^4 Ai = A0 \cap \!\, A1 \cap \!\, A2 \cap \!\, A3 \cap \!\, A4 =  {a \in \!\, \mathbb{Z} \!\, | a <= 0 }



On Tue, Sep 14, 2010 at 9:05 PM, Aaron Albers <aaronc...@gmail.com> wrote:

Aaron Albers

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Sep 14, 2010, 11:37:03 PM9/14/10
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(c) A3 \cap \!\, (A-3)^c = A3 \ A-3 = { -2, -1, 0, 1, 2, 3 }

On Tue, Sep 14, 2010 at 9:05 PM, Aaron Albers <aaronc...@gmail.com> wrote:

alex

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Sep 15, 2010, 2:39:05 PM9/15/10
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wouldn't this be from -∞ to -3.  since a ≤ n

alex

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Sep 15, 2010, 2:39:59 PM9/15/10
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i spoke too early. i just read your next posting. goodness i need to read all of it before i post anything redundant. 

Anne S

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Sep 15, 2010, 2:50:14 PM9/15/10
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Hey Aaron -- there are tags in your post that don'g seem to be coming
through for me. For example [image: \cap \!\,] Are you sending images
in your messages?



On Sep 14, 9:28 pm, Aaron Albers <aaroncalb...@gmail.com> wrote:
> I take it back.
>
> The only intersection that A3 [image: \cap \!\,] A-3 has is -3 to -infinity
>
> A3 [image: \cap \!\,] A-3 = {a [image: \in \!\,] [image: \mathbb{Z} \!\,] |
> a <= -3 }
>
> On Tue, Sep 14, 2010 at 9:07 PM, Aaron Albers <aaroncalb...@gmail.com>wrote:
>
> > (b) A3 [image: \cap \!\,] A-3
> >  This would go from -3 to 3
>
> >  A3 [image: \cap \!\,] A-3 = {-3, -2 -1, 0, 1, 2, 3}
>

Diane

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Sep 15, 2010, 9:22:30 PM9/15/10
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Anne,

If you open the emails google groups sends out, you can select show
images and it becomes much more readable.

anne speck

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Sep 15, 2010, 9:26:19 PM9/15/10
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Much better! Thank you!



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