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Single Idea 9681
[filed under theme 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
]
Full Idea
X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X).
Gist of Idea
X = Y means the set X equals the set Y
Source
Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
Book Ref
Priest,Graham: 'Introduction to Non-Classical Logic' [CUP 2001], p.-6
The
27 ideas
from 'Intro to Non-Classical Logic (1st ed)'
9672
|
Free logic is one of the few first-order non-classical logics
[Priest,G]
|
9697
|
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
[Priest,G]
|
9685
|
<a,b&62; is a set whose members occur in the order shown
[Priest,G]
|
9695
|
An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
[Priest,G]
|
9696
|
A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
[Priest,G]
|
9686
|
A 'set' is a collection of objects
[Priest,G]
|
9687
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A 'member' of a set is one of the objects in the set
[Priest,G]
|
9675
|
a ∈ X says a is an object in set X; a ∉ X says a is not in X
[Priest,G]
|
9674
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{x; A(x)} is a set of objects satisfying the condition A(x)
[Priest,G]
|
9673
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{a1, a2, ...an} indicates that a set comprising just those objects
[Priest,G]
|
9677
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Φ indicates the empty set, which has no members
[Priest,G]
|
9676
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{a} is the 'singleton' set of a (not the object a itself)
[Priest,G]
|
9688
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A 'singleton' is a set with only one member
[Priest,G]
|
9689
|
The 'empty set' or 'null set' has no members
[Priest,G]
|
9690
|
A set is a 'subset' of another set if all of its members are in that set
[Priest,G]
|
9691
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A 'proper subset' is smaller than the containing set
[Priest,G]
|
9680
|
The empty set Φ is a subset of every set (including itself)
[Priest,G]
|
9679
|
X⊂Y means set X is a 'proper subset' of set Y
[Priest,G]
|
9678
|
X⊆Y means set X is a 'subset' of set Y
[Priest,G]
|
9681
|
X = Y means the set X equals the set Y
[Priest,G]
|
9683
|
X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
[Priest,G]
|
9682
|
X∪Y indicates the 'union' of all the things in sets X and Y
[Priest,G]
|
9684
|
Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X
[Priest,G]
|
9694
|
The 'relative complement' is things in the second set not in the first
[Priest,G]
|
9693
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The 'intersection' of two sets is a set of the things that are in both sets
[Priest,G]
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9692
|
The 'union' of two sets is a set containing all the things in either of the sets
[Priest,G]
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9698
|
The 'induction clause' says complex formulas retain the properties of their basic formulas
[Priest,G]
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