this post was submitted on 29 Nov 2024
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Incorrect. There are complex valued metric spaces
And even if we assume real valued metrics, then i usually represents the unit vector (0,1) which has distance real 1.
That's NOT a metric. That's a measure. Two wholly different things.
It can be a pseudometric
That's more related to a metric but it still can't be complex valued and it's still not a measure.