REAL ANALYSIS I
REAL ANALYSIS I M 365C
Popular in Course
Popular in Mathematics (M)
This 1 page Class Notes was uploaded by Reyes Glover on Sunday September 6, 2015. The Class Notes belongs to M 365C at University of Texas at Austin taught by Kenneth Chu in Fall. Since its upload, it has received 83 views. For similar materials see /class/181447/m-365c-university-of-texas-at-austin in Mathematics (M) at University of Texas at Austin.
Reviews for REAL ANALYSIS I
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/06/15
ZermeloFraenkel Choice ZFC Set Theory Axioms If 1 Empty Set Axiom There exists a set Q which contains no elements 2 Extension Axiom Two sets are identical if they have the same elements 3 Pair Axiom If x y are sets then there is a set x y whose elements are x and y 4 Union Axiom If x is a set of sets then there exists a set U 3 whose elements are the elements of the elements of x 5 Power Set Axiom If x is a set then there exists a set 79x whose elements are the subsets of x 6 Selection Axiom Let a be a set and let qb be a quotstatementquot involving one free variable 3 Then there exists a set b whose elements are the elements as of a such that qbx is true ie b x E a I is true 7 Replacement Axiom Let a be a set and 11x y be a statment involving two free variables such that for any 3 there exists at most one y that satisfies 11x y Then I y 11xy holds for some 10 E a iS a set 8 Axiom of Infinity There exists a set a such that Q E a and x E a whenever x E a 9 Foundation Axiom For any nonempty set 3 there exists y E x such that x m y Q I This axiom prevents Russel s paradox 10 The Axiom of Choice AC p 1
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'