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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST

[symbols which are distinctive of set theory]

19 ideas
'fld R' indicates the 'field' of all objects in the relation [Enderton]
'dom R' indicates the 'domain' of objects having a relation [Enderton]
'ran R' indicates the 'range' of objects being related to [Enderton]
We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton]
'F(x)' is the unique value which F assumes for a value of x [Enderton]
∈ relates across layers, while ⊆ relates within layers [Hart,WD]
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G]
<a,b&62; is a set whose members occur in the order shown [Priest,G]
{a1, a2,} indicates that a set comprising just those objects [Priest,G]
a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G]
{x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G]
{a} is the 'singleton' set of a (not the object a itself) [Priest,G]
Φ indicates the empty set, which has no members [Priest,G]
X = Y means the set X equals the set Y [Priest,G]
X⊂Y means set X is a 'proper subset' of set Y [Priest,G]
X⊆Y means set X is a 'subset' of set Y [Priest,G]
X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G]
Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G]
X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G]