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Levi Pearson 2014-01-25 13:59:36 -07:00
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@ -34,3 +34,35 @@ E.g. $\{2,4,5,8\} = \{4,2,8,6\}$ but $\{2,4,6,8\} \neq \{2,4,6,7\}$.
Uppercase letters often denote sets, e.g. $A = \{1,2,3,4\}$. Uppercase letters often denote sets, e.g. $A = \{1,2,3,4\}$.
To express membership, we use $\in$, as in $2 \in A$. To express membership, we use $\in$, as in $2 \in A$.
To express non-membership, we use $\notin$, as in $5,6 \notin A$.
**Special Sets**
$\Bbb{N}$
: *natural numbers*, the positive whole numbers $\{1,2,3,4,5,\dots\}$
$\Bbb{Z}$
: *integers*, $\{\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4,\dots\}$
$\Bbb{Q}$
: *rational numbers*, $\Bbb{Q} = \{x : x = \frac mn, m,n \in \Bbb{Z}
and n \neq 0\}$.
$\Bbb{R}$
: *real numbers*, the set of all real numbers on the number line.
$\emptyset$
: *empty set*, the unique set with no members, $\{\}$
* * * *
For finite sets $X$, $|X|$ represents the *cardinality* or *size* of
the set, which is the number of elements it has. E.g. $|A| = 4$.
*set-builder notation* describes sets that are too big or complex to
be listed out. E.g. the infinite set of even integers: $$
E = \{2n : n \in \Bbb{Z}\}
$$
This can be read as "E is the set of all things of form $2n$, such
that $n$ is an element of $\Bbb{Z}$."