Why does one take $\inf ||x-a||$ for $d(x,A)$?
Why not just take exactly $||x-a||$? Or $\sup ||x-a||$ (this would not offer measurability though, because it could "explode" to a very big number)?
2026-03-25 23:33:05.1774481585
Why does one take $\inf ||x-a||$ for $d(x,A)$?
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I think that you are mixing two concepts here. If $x$ is a point in a normed vector space: