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January 5th, 2017, 01:19 PM   #1
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Set Builder Notation?

Hi everybody. I'm currently trying to understand the principles of set builder notation. I understand that "(" is used for < and > and "[" is used for less than or equal to and greater than or equal to. But I am looking at a question which says; "Use set builder notation to give a description of each of these
three (3) sets. Assume a domain of integers."

I. { 0, 4, 8, 12, 16}
II. {−6,−4,−2, 0, 2, 4, 6}

It doesn't actually tell me what the condition for the set is though such as "x | x > 4" or something like that so I'm confused as to what the answers to these questions would be. I'm probably missing something so if somebody could help me that that would be much appreciated, thanks.
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January 5th, 2017, 01:33 PM   #2
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I. $\{0, 4, 8, 12, 16\} = \{x : x = 4 k,~k \in \mathbb{Z} \wedge 0\leq k \leq 4\}$

II. $\{−6,−4,−2, 0, 2, 4, 6\} = \{x : x=2k,~k\in \mathbb{Z} \wedge -3 \leq k \leq 3\}$

another slightly more elegant way of expressing this is

$\{x : x=2k,~k\in \mathbb{Z} \wedge |k|\leq 3 \}$
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January 5th, 2017, 02:14 PM   #3
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( and [ are used when referring to continuous sets. Not meaningful for discrete sets.
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