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Single Idea 9705
[filed under theme 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
]
Full Idea
'fld R' indicates the 'field' of a relation, that is, the set of all objects that are members of ordered pairs on either side of the relation.
Gist of Idea
'fld R' indicates the 'field' of all objects in the relation
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0)
Book Ref
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.4
The
19 ideas
with the same theme
[symbols which are distinctive of set theory]:
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9703
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'dom R' indicates the 'domain' of objects having a relation
[Enderton]
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9705
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'fld R' indicates the 'field' of all objects in the relation
[Enderton]
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9704
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'ran R' indicates the 'range' of objects being related to
[Enderton]
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9710
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We write F:A→B to indicate that A maps into B (the output of F on A is in B)
[Enderton]
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9707
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'F(x)' is the unique value which F assumes for a value of x
[Enderton]
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13443
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∈ relates across layers, while ⊆ relates within layers
[Hart,WD]
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9697
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X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
[Priest,G]
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9685
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<a,b&62; is a set whose members occur in the order shown
[Priest,G]
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9675
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a ∈ X says a is an object in set X; a ∉ X says a is not in X
[Priest,G]
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9674
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{x; A(x)} is a set of objects satisfying the condition A(x)
[Priest,G]
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9673
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{a1, a2, ...an} indicates that a set comprising just those objects
[Priest,G]
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9677
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Φ indicates the empty set, which has no members
[Priest,G]
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9676
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{a} is the 'singleton' set of a (not the object a itself)
[Priest,G]
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9679
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X⊂Y means set X is a 'proper subset' of set Y
[Priest,G]
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9678
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X⊆Y means set X is a 'subset' of set Y
[Priest,G]
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9681
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X = Y means the set X equals the set Y
[Priest,G]
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9683
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X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
[Priest,G]
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9682
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X∪Y indicates the 'union' of all the things in sets X and Y
[Priest,G]
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9684
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Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X
[Priest,G]
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