# Thread: is this sequence convergent in this vector space

1. ## is this sequence convergent in this vector space

$(1,0,0,....), (0,1,0,0,....) , ...........$

V is the vector space of all sequences of real numbers converge to zero.
and norm: $|(x_{1},x_{2},....)|=\max_{i\geq1}{|x_{i}|}$

2. Originally Posted by silversand
$(1,0,0,....), (0,1,0,0,....) , ...........$

V is the vector space of all sequences of real numbers converge to zero.
and norm: $|(x_{1},x_{2},....)|=\max_{i\geq1}{|x_{i}|}$
No, that sequence does not converge because it is not Cauchy. The distance between any two elements of the sequence (as measured by the norm of their difference) is 1.