Definition The set of all functions from X to Y: yx={flf:X→Y} Q:Is there a set consisting of all functions? 4口￥0,3，t夏里Q0 马骏(majunnju.edu.cm)1-10 Set Theory(I):Functions2021年12月09日11/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Q : Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X, there exists a function IX : {X} → {X}. ∪ IX∈A dom(IX) 马骏 (majun@nju.edu.cn) 1-10 Set Theory (III): Functions 2021 年 12 月 09 日 11 / 40
Definition The set of all functions from X to Y: yx={fIf:X→Yy Q:Is there a set consisting of all functions? Theorem There is no set consisting of all functions. 4口￥0,3，t夏里Q0 马驶(majun&inju.edu.cm)） 1-10 Set Theory(I):Functions2021年12月09日11/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Q : Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X, there exists a function IX : {X} → {X}. ∪ IX∈A dom(IX) 马骏 (majun@nju.edu.cn) 1-10 Set Theory (III): Functions 2021 年 12 月 09 日 11 / 40
Definition The set of all functions from X to Y: yx={fIf:X→Yy Q:Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. 4口￥0,3，t夏里Q0 马驶(majun&inju.edu.cm) 1-10 Set Theory(I):Functions2021年12月09日11/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Q : Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X, there exists a function IX : {X} → {X}. ∪ IX∈A dom(IX) 马骏 (majun@nju.edu.cn) 1-10 Set Theory (III): Functions 2021 年 12 月 09 日 11 / 40
Definition The set of all functions from X to Y: Yx={fIf:X→Y} Q:Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X,there exists a function Ix :X. 4口￥0,3，t夏里Q0 马驶(majun&inju.edu.cm) 1-10 Set Theory(II:Functions2021年12月09日11/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Q : Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X, there exists a function IX : {X} → {X}. ∪ IX∈A dom(IX) 马骏 (majun@nju.edu.cn) 1-10 Set Theory (III): Functions 2021 年 12 月 09 日 11 / 40
Definition The set of all functions from X to Y: Yx={flf:X→Y} Q:Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X,there exists a function Ix :X. dom(Ix) IxEA 4口·￥①，43，t夏，里Q0 马驶(majun&inju.edu.cm) 1-10 Set Theory (III):Functions 2021年12月09日11/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Q : Is there a set consisting of all functions? Theorem There is no set consisting of all functions. Suppose by contradiction that A is the set of all functions. For every set X, there exists a function IX : {X} → {X}. ∪ IX∈A dom(IX) 马骏 (majun@nju.edu.cn) 1-10 Set Theory (III): Functions 2021 年 12 月 09 日 11 / 40