Fixed some notation

master
Levi Pearson 2014-01-25 15:25:44 -07:00
parent a683e64fb9
commit c2017edf36
1 changed files with 6 additions and 6 deletions

View File

@ -139,7 +139,7 @@ A,i \in \{1,\dots,n\}\} $$
**Definition 1.3** **Definition 1.3**
: $A$ and $B$ are sets. If every element of $A$ is also an element of : $A$ and $B$ are sets. If every element of $A$ is also an element of
$B$, then $A$ is a *subset* of $B$ and we write $A \subseteq B$. If $B$, then $A$ is a *subset* of $B$ and we write $A \subseteq B$. If
this is not the case, we write $A \subsetneq B$, which means there is this is not the case, we write $A \not\subseteq B$, which means there is
at least one element of $A$ that is not in $B$. at least one element of $A$ that is not in $B$.
**Fact 1.2** **Fact 1.2**
@ -161,7 +161,7 @@ $2^n$ total leaves of the tree.
1. Subsets of \{1,2,3,4\}: $\emptyset, \{1\}, \{2\}, \{3\}, \{4\}, 1. Subsets of \{1,2,3,4\}: $\emptyset, \{1\}, \{2\}, \{3\}, \{4\},
\{1,2\}, \{1,3\}, \{1,4\}, \{2,3\}, \{2,4\}, \{3,4\}, \{1,2,3\}, \{1,2\}, \{1,3\}, \{1,4\}, \{2,3\}, \{2,4\}, \{3,4\}, \{1,2,3\},
\{1,2,4\}, \{1,3,4\}, \{2,3,4\}, \{1,2,3,4\} \{1,2,4\}, \{1,3,4\}, \{2,3,4\}, \{1,2,3,4\}$
* * * * * * * *
@ -200,9 +200,9 @@ as the set of points in a circle $C$, the universe would be
$\Bbb{R}^2$. $\Bbb{R}^2$.
**Definition 1.6** **Definition 1.6**
: $A$ is a set in the universe $U$. The *complement* of $A$ or $A\bar$ : $A$ is a set in the universe $U$. The *complement* of $A$ or $\bar A$
is the set $A\bar = U - A$. is the set $\bar A = U - A$.
E.g. if $P$ is the set of prime numbers, then $$ E.g. if $P$ is the set of prime numbers, then $$
P\bar = \Bbb{N} - P = \{1,4,6,8,9,10,12,\dots\} \bar P = \Bbb{N} - P = \{1,4,6,8,9,10,12,\dots\}
$$ so $P\bar$ is the set of composite numbers and 1. $$ so $\bar P$ is the set of composite numbers and 1.