MathItems

Proof P80 of T22

Let ε>0\varepsilon > 0 be given. There exists integers NN, NN' such that

Hence if nmax(N,N)n \geq \max(N, N'), we have

d(p,p)d(p,pn)+d(pn,p)<ε  .d(p,p') \leq d(p,p_n) + d(p_n,p') < \varepsilon \; .

Since ε\varepsilon was arbitrary, we conclude that d(p,p)=0d(p,p') = 0.