Definition The set of all functions from X to Y: Yx={f|f:X→Y Q:Is there a set consisting of all functions? 4口￥0,43，t夏里Q0 Hengfong Wei Chkweinjn.ed.cn 1-10 Set Theory (III):Functions 2019 12 10 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) Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 11 / 40
Definition The set of all functions from X to Y: Yx={f|f:X→Y 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 Hengfong Wei Chkweinjn.ed.cn 1-10 Set Theory (III):Functions 2019 12 10 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) Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 11 / 40
Definition The set of all functions from X to Y: Yx={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. 4口￥0,43，t夏里Q0 Hengfeng Wei (hfweinju.edu.cn)1-10 Set Theory (III):Functions 2019年12月10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) Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 11 / 40
Definition The set of all functions from X to Y: Yx={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. 4口￥0,3，t夏里Q0 Hengfong Wei Chkweinjn.ed.cn 1-10 Set Theory (III):Functions 2019 12 10 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) Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 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. dom(Ix) Ix∈A 4口·￥①，43，t夏里0Q0 Hengfeng Wei (hfweiinju.edu.cn)1-10 Set Theory (III):Functions 2019年12月10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) Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 11 / 40