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Single Idea 10813
[filed under theme 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
]
Full Idea
A new student of set theory has just one thing, the element, and he has another single thing, the singleton, and not the slightest guidance about what one thing has to do with the other.
Gist of Idea
What on earth is the relationship between a singleton and an element?
Source
David Lewis (Mathematics is Megethology [1993], p.12)
Book Ref
-: 'Philosophia Mathematica' [-], p.12
The
12 ideas
with the same theme
[status of a set having a single member]:
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15505
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If a set is 'a many thought of as one', beginners should protest against singleton sets
[Cantor, by Lewis]
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6103
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Normally a class with only one member is a problem, because the class and the member are identical
[Russell]
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13203
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The singleton is defined using the pairing axiom (as {x,x})
[Enderton]
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10813
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What on earth is the relationship between a singleton and an element?
[Lewis]
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10814
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Are all singletons exact intrinsic duplicates?
[Lewis]
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15497
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We can replace the membership relation with the member-singleton relation (plus mereology)
[Lewis]
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15506
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If we don't understand the singleton, then we don't understand classes
[Lewis]
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15511
|
If singleton membership is external, why is an object a member of one rather than another?
[Lewis]
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15513
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Maybe singletons have a structure, of a thing and a lasso?
[Lewis]
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9551
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What is special about Bill Clinton's unit set, in comparison with all the others?
[Chihara]
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8956
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What is a singleton set, if a set is meant to be a collection of objects?
[Szabó]
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14243
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The unit set may be needed to express intersections that leave a single member
[Oliver/Smiley]
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