9 Zbiory równoliczne.pdf

(119 KB) Pobierz
litm.dvi
9
9 A
9 F
9 H
9 K
9 M
9 N
69698162.015.png 69698162.016.png
*
u
v
u
v
f : u
→
v
u
v
*
S(u) S(v) P(u) P(v)
u
*
u
v
v
u
u v
*
u
f : u
→
P(u)
v = {x∈u : x /∈f(x)}
v∈f[u]
y∈u
v = f(y)
y∈v
v
y /∈f(y) = v
y /∈v
v
y∈f(y) = v
v /∈f(u)
f
2
9
9 A
69698162.017.png 69698162.018.png 69698162.001.png 69698162.002.png
u
v
v
u
u v
f : u
→
v
g : v
→
T
u
h : P(u)
→
P(u)
h(w) = u\g[v\f[w]]
u 0 =
{w⊆u : h(w)⊆w}
u 0
h(u)⊆u
u 1 ⊆u 2 ⊆u
f[u 1 ]⊆f[u 2 ]
v \ f[u 2 ]⊆v \ f[u 1 ]
g[v \ f[u 2 ]]⊆g[v \ f[u 1 ]]
\
\
h(u 1 )⊆h(u 2 )
\
h(u 0 ) = h(
{w : h(w)⊆w})⊆
{h(w): h(w)⊆w}⊆
{w : h(w)⊆w} = u 0 .
h(w)⊆w
u 0 ⊆w u 0 ⊆h(u 0 )
h(u 0 )⊆u 0
h(h(u 0 ))⊆h(u 0 )
h(u 0 ) = u 0
e : u
→
v
e(x) =
f(x)
x∈u 0
g −1 (x)
x∈u \ u 0
e
u \ u 0 = g[v \ f[u 0 ]]
e
h(u 0 ) = u 0
g −1 [u \ u 0 ] = v \ f[u 0 ]
e[u] = f[u 0 ]∪g −1 [u \ u 0 ] = v
9
9 B
69698162.003.png 69698162.004.png 69698162.005.png 69698162.006.png
e
f
g −1
f[u 0 ]∩g −1 [u \ u 0 ] =∅
2
n
)
n
n =
⇒
)
m > 0
f : m + 1
→
m
g : m
→
m − 1
f(x)
g(x) =
x = f −1 (m − 1)
f(m)
x = f −1 (m − 1)
n =
(1) n <
n + 1≤
n
n + 1
n
n + 1
n + 1⊆
(2) < n +1≤n +1 +1
n⊆n + 1
⊆ + 1
+ 1⊆n
< n
∈!
2
9
9 C
(
⇐
(
69698162.007.png 69698162.008.png 69698162.009.png 69698162.010.png
u
g : P(u) \ {∅}
→
u
g(v)∈v v⊆
u
v =∅
f( )( ) =
g(u \ f( )[ ]) u \ f( )[ ] =∅
(f( ) ) <
f( ) = f( )|
<
v
x∈u
f(S( ))( ) = x
u⊆f(S( ))[S( )]
(f(S( )) )
u
'(x, )
f(S( ))( ) = x
<
f(S( ))( ) =
f(S( ))( ) = f(S( ))( )
x∈v
'(x, )
w
∈w
'(x, )
x
w
9
9 D
u
69698162.011.png 69698162.012.png 69698162.013.png 69698162.014.png

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin