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Single Idea 9707
[filed under theme 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
]
Full Idea
F(x) is a 'function', which indicates the unique value which y takes in ∈ F. That is, F(x) is the value y which F assumes at x.
Gist of Idea
'F(x)' is the unique value which F assumes for a value of x
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.5
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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