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Notes Enderton Elements of Set Theory
10-27-2016, 11:27 AM
Post: #1
Notes Enderton Elements of Set Theory
1 Introduction

Baby Set Theory

A set is a collection of things (called its members or elements),
the collection being regarded as a single object. We write " $t\in A$"
to say that t is a member of $A$, and we write " $t \not\in A$" to say that
t is not a member of $A$.

Principle of Extensionality If two sets have exactly the same
members, then they are equal. $\small(A=B)\iff((x\in A)\iff(x\in B))$

Empty Set is denoted by $\varnothing.$ Which has no elements/members.

Power set $\mathscr{P}A = \{E\mid E\subset A\}\;$is the set of all subsets of $A\underset{\,}{\;}$:
$\mathscr{P}\varnothing = \{\varnothing\},\;\mathscr{P}\{\varnothing\}=\{\varnothing,\{\varnothing\}\},\; \mathscr{P}\{0,1\}=\{\varnothing,\{0\},\{1\},\{0,1\}\}.$
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