EDB — 0MT

[0MT] Given a sequence \((x_ n)_ n⊆ X\) and \(x∈ X\),

• we will say that ”\((x_ n)_ n\) converges to \(x\)” if \(\lim _ n d(x_ n,x)=0\); we will also write \(x_ n→_ n x\) to indicate that the sequence converges to \(x\).

• We will say that ”\((x_ n)_ n\) is a Cauchy sequence” if

  \[ ∀ \varepsilon {\gt}0~ ~ ∃ N∈ℕ~ ,~ ∀ n,m≥ N~ ~ d(x_ n,x_ m){\lt}\varepsilon ~ ~ . \]