you cannot do that: the euclidean norm is not defined for an infinite-dimensional space.
Why not? It is the square root of the sum of (dxi)^2, where i goes through all dimensions. Sometimes it is a finite value. Otherwise the distance is infinite.
The points T0(0,0,0,0....) and T1(0,1/sqrt(2),1/sqrt(4),1/sqrt(8)...) are 1 apart.
Why not? It is the square root of the sum of (dxi)^2, where i goes through all dimensions. Sometimes it is a finite value. Otherwise the distance is infinite.
The points T0(0,0,0,0....) and T1(0,1/sqrt(2),1/sqrt(4),1/sqrt(8)...) are 1 apart.
A metric is supposed to be always finite. Note the round right bracket in https://en.wikipedia.org/wiki/Metric_(mathematics)#Definition.
Fixed link.
This is probably not the intended link.