### Ideas from 'Elements of Set Theory' by Herbert B. Enderton , by Theme Structure

#### [found in 'Elements of Set Theory' by Enderton,Herbert B. [Posts + Telecoms 2006,7-115-14550-4]].

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###### 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
 13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other
 13204 The 'ordered pair' is defined to be {{x}, {x,y}}
 13206 A 'linear or total ordering' must be transitive and satisfy trichotomy
###### 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
 13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ
 13199 The empty set may look pointless, but many sets can be constructed from it
###### 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
 13203 The singleton is defined using the pairing axiom (as {x,x})
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
 13202 Fraenkel added Replacement, to give a theory of ordinal numbers
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
 13205 We can only define functions if Choice tells us which items are involved