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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.