Category:Elementary Set Theory Theorems

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Pages in category "Elementary Set Theory Theorems"

The following 18 pages are in this category, out of 18 total.

A

  • A cap (B-C) = (A cap B) - C
  • A pair of identical elements is a singleton
  • A-(A-B) = A cap B

D

  • Distributivity of intersections across unions

E

  • Equivalence classes are either equal or disjoint
  • Equivalent conditions to a set being saturated with respect to a function

E cont.

  • Equivalent conditions to a set being saturated with respect to a map
  • Every surjective map gives rise to an equivalence relation

F

  • Factoring a function through the projection of an equivalence relation induced by that function yields an injection
  • Function factorisation

G

  • Greater than or equal to/Epsilon form

I

  • If the composition of two functions is a bijection then the initial map is injective and the latter map is surjective

I cont.

  • Index of elementary set theory equalities
  • Intersection is commutative

P

  • Passing to the quotient (function)
  • Properties of classes of sets closed under set-subtraction
  • Properties of the pre-image of a map

T

  • The intersection of two sets is non-empty if and only if there exists a point in one set that is in the other set
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Categories:
  • Theorems
  • Set Theory Theorems
  • Elementary Set Theory

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