Combining Texts
Ideas for
'works', 'What Required for Foundation for Maths?' and 'Journals'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
13 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
|
15901
|
Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine]
|
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
|
13444
|
Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
|
|
18098
|
Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
|
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
|
15505
|
If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
|
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
|
10701
|
Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter]
|
|
10865
|
The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
|
17795
|
Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry]
|
|
17796
|
There is a semi-categorical axiomatisation of set-theory [Mayberry]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
|
13016
|
The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
|
17800
|
The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry]
|
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / b. Combinatorial sets
|
14199
|
Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley]
|
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
|
17801
|
The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry]
|
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
|
17803
|
Limitation of size is part of the very conception of a set [Mayberry]
|