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I was wondering about the meaning of the infinity norm

[itex]|| x ||_\inf= max\{|x_1|, |x_2|....|x_n| \}[/itex]

if a norm is a function that assigns a strictly positive length or size to all vectors in a vector space, why do we assign the maximum (or sup) as the value of this norm ?

It must be a very basic or obvious answer because I cannot find in any text.

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# Infinity norm why ?

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