Combining Texts
Ideas for
'Parmenides', 'Ambitious, yet modest, Metaphysics' and 'Intro to Non-Classical Logic (1st ed)'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
26 ideas
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
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]
|
9675
|
a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G]
|
9674
|
{x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G]
|
9673
|
{a1, a2, ...an} indicates that a set comprising just those objects [Priest,G]
|
9677
|
Φ indicates the empty set, which has no members [Priest,G]
|
9676
|
{a} is the 'singleton' set of a (not the object a 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]
|
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9688
|
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
|
A 'proper subset' is smaller than the containing set [Priest,G]
|
9694
|
The 'relative complement' is things in the second set not in the first [Priest,G]
|
9693
|
The 'intersection' of two sets is a set of the things that are in both sets [Priest,G]
|
9692
|
The 'union' of two sets is a set containing all the things in either of the sets [Priest,G]
|
9698
|
The 'induction clause' says complex formulas retain the properties of their basic formulas [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
|
A 'member' of a set is one of the objects in the set [Priest,G]
|
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
9680
|
The empty set Φ is a subset of every set (including itself) [Priest,G]
|