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Single Idea 9692
[filed under theme 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
]
Full Idea
The 'union' of two sets is a set containing all the things in either of the sets
Gist of Idea
The 'union' of two sets is a set containing all the things in either of the sets
Source
Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
Book Ref
Priest,Graham: 'Introduction to Non-Classical Logic' [CUP 2001], p.-6
The
37 ideas
from Graham Priest
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9123
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Someone standing in a doorway seems to be both in and not-in the room
[Priest,G, by Sorensen]
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9672
|
Free logic is one of the few first-order non-classical logics
[Priest,G]
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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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9695
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An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
[Priest,G]
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9696
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A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
[Priest,G]
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9686
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A 'set' is a collection of objects
[Priest,G]
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9687
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A 'member' of a set is one of the objects in the set
[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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9688
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A 'singleton' is a set with only one member
[Priest,G]
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9689
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The 'empty set' or 'null set' has no members
[Priest,G]
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9690
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A set is a 'subset' of another set if all of its members are in that set
[Priest,G]
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9691
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A 'proper subset' is smaller than the containing set
[Priest,G]
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9680
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The empty set Φ is a subset of every set (including 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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9694
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The 'relative complement' is things in the second set not in the first
[Priest,G]
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9693
|
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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13366
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The least ordinal greater than the set of all ordinals is both one of them and not one of them
[Priest,G]
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13367
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The next set up in the hierarchy of sets seems to be both a member and not a member of it
[Priest,G]
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13368
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The 'least indefinable ordinal' is defined by that very phrase
[Priest,G]
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13370
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'x is a natural number definable in less than 19 words' leads to contradiction
[Priest,G]
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13369
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By diagonalization we can define a real number that isn't in the definable set of reals
[Priest,G]
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13371
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If you know that a sentence is not one of the known sentences, you know its truth
[Priest,G]
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13372
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There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar
[Priest,G]
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13373
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Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong
[Priest,G]
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8720
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A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions
[Priest,G, by Friend]
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