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a an+1 −an
a
K E
(un)K
(un)un+1
2u2n→0
a(un)−2a
(un)
un+u2n
2n≥0

A a
A
∀α < β ∈A, [α;β]⊂A
α < β ∈A γ ∈[α;β]γ=α γ =β γ ∈A
γ∈]α;β[
N∈Nε > 0an+1 −an→0N0
∀n≥N0,|an+1 −an| ≤ ε
α a α < γ p ≥max(N, N0)
ap< γ q ≥max(N, N0)aq> γ
p<q
E={n∈Jp;qK, an< γ}
ENp∈E q
r r < q aq≥γ
r∈E r + 1 /∈E ar< γ ≤ar+1 |γ−ar|≤|ar+1 −ar| ≤ ε
p>q
∀N∈N,∀ε > 0,∃r≥N, |γ−ar| ≤ ε
γ a
(un)K `
(un)`
∃ε > 0,∀N∈N,∃n≥N, |un−`|> ε
|un−`|> ε
(un)
K
`
|un−`|> ε
εn=un+1
2u2n→0
uϕ(n)→a u2ϕ(n)= 2εϕ(n)−2uϕ(n)→ −2a
a∈Adh(u) =⇒ −2a∈Adh(u)
(un)a k ∈N
(−2)ka(un)
(un)un→0
`= limn→+∞un+u2n
2vn=un−2 3` εn=vn+v2n 2→0
a(vn)
ϕ:N→Nvϕ(n)→a
v2ϕ(n)= 2εϕ(n)−2vϕ(n)−−−−−→
n→+∞−2a
−2a(vn)
p∈N(−2)pa(vn)
(un) (vn)
a= 0
(vn)
(vn) [−ε;ε], ε > 0