Definition The set of all functions from X to Y: Yx={f|f:X→Y} Yx={f∈P(X×Y)|f:X→Y} X and Y are finite sets with x and y elements,respectively. IXI=z IYI=y,IYXI= 4口￥0,43，t夏，里Q0 Hengeng Wei bhkweionjn.edu.cn 1-10 Set Theory (II):Functions 2019 12 10 8/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Y X = {f ∈ P(X × Y ) | f : X → Y } X and Y are finite sets with x and y elements, respectively. |X| = x |Y | = y, |Y X| = y x Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 8 / 40
Definition The set of all functions from X to Y: Yx={f|f:X→Y} Yx={f∈P(X×Y)|f:X→Y} X and Y are finite sets with x and y elements,respectively. IXI=z IYI=y,IYx=y 4口·￥①，43，t夏，3)Q0 Hengeng Wei bhkweionjn.edu.cn 1-10 Set Theory (II):Functions 2019 12 10 8/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } Y X = {f ∈ P(X × Y ) | f : X → Y } X and Y are finite sets with x and y elements, respectively. |X| = x |Y | = y, |Y X| = y x Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 8 / 40
Definition The set of all functions from X to Y: Yx={fIf:X→Y} Y:y0= 4口￥0,43，t夏，里Q0 Hengeng Wei thkweionjn.edu.cn 1-10 Set Theory (II):Functions 2019 12 10 9/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } ∀Y : Y ∅ = {∅} ∅ ∅ = {∅} ∀X ̸= ∅ : ∅ X = ∅ Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 9 / 40
Definition The set of all functions from X to Y: Yx={f|f:→Y} y:y0={0 4口￥0,43，t夏，里Q0 Hengeng Wei thkweionjn.edu.cn 1-10 Set Theory (II):Functions 2019 12 10 9/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } ∀Y : Y ∅ = {∅} ∅ ∅ = {∅} ∀X ̸= ∅ : ∅ X = ∅ Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 9 / 40
Definition The set of all functions from X to Y: Yx={fIf:X→Y} y:y0={0 0°={01 4口￥0,43，t夏，里Q0 Hengfeng Wei (hfweiinju.edu.cn)1-10 Set Theory (III):Functions 2019年12月10日9/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition The set of all functions from X to Y : Y X = {f | f : X → Y } ∀Y : Y ∅ = {∅} ∅ ∅ = {∅} ∀X ̸= ∅ : ∅ X = ∅ Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 9 / 40