Semaine 9

E, F, G
u:E→F v :F→G
v◦u u
v◦u v
f:E→F g :F→G h :G→E h ◦g◦f g ◦f◦h f ◦h◦g
f, g h
a∈R
(∀≥0,|a|< )⇒a= 0.
(∀ > 0,|a|< )⇒a= 0.
E
a∈EP(P({a})).
A, B ∈ P(E) (A\B)∪B6=A
E A, B, C E A∆B= (A\B)∪(B\A).
A∆B= (A∪B)\(A∩B).
A∆B=A∆C⇔B=C.
A∆B=A∩B⇒A=B=∅.
E f :E→E
f◦f=f
f f =idE
f f =idE
f◦f◦f=f f
f:E→F g :E→G
h:E→F×G
x7→ (f(x), g(x)).
f g h
h f g
√p p
E A, B, C E
A=B⇔A∩B=A∪B
A∪B=A∩C⇔B⊂A⊂C.
A∪B=A∪C A ∩B=A∩C⇔B=C.
E A, B E
f:P(E)→ P(A)× P(B)
X7→ (X∩A, X ∩B).
f A ∪B=E.
f A ∩B=∅.
f