Difference between revisions of "Subset"
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| − | The set of all subsets of a given set <math>S</math> is called the [[power set]] of <math>S</math> and is denoted <math>\mathcal{P}(S)</math>. | + | The set of all subsets of a given set <math>S</math> is called the [[power set]] of <math>S</math> and is denoted <math>\mathcal{P}(S)</math> or <math>2^S</math>. |
== Example Problems == | == Example Problems == | ||
Revision as of 12:11, 24 August 2006
We say a set 
is a subset of another set 
if every element of is also an element of , and we denote this by $A \sub B$ (Error compiling LaTeX. Unknown error_msg). The empty set is a subset of every set, and every set is a subset of itself. The notation 
emphasizes that may be equal to , while 
says that is any subset of other than itself.
The following is a true statement:
$\emptyset \sub \{1, 2\} \sub \mathbb{N} \sub \mathbb{Z} \sub \mathbb{Q} \sub \mathbb{R} \sub \mathbb{C} \sub \mathbb{C}\, \cup\{\textrm{Groucho, Harpo, Chico}\} \supset \{1, 2, i, \textrm{Groucho}\}$ (Error compiling LaTeX. Unknown error_msg)
The set of all subsets of a given set 
is called the power set of and is denoted 
or 
.
