Here's a question from Apostol's Calculus Vol1(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that instead of the usual definition of norm of a vector in [tex]V_n[/tex], we define it the following way,

[tex]||A|| = \sum_{k=1}^{n}|a_k|.[/tex]

Using this definition in [tex]V_2[/tex] describe on a figure the set of all points [tex](x,y)[/tex] of norm 1.

Is it possible to do that? Doesn't every point [tex](x,y)[/tex] of the form [tex](\frac{1}{s}, \frac{s-1}{s}), s \geq 1[/tex] satisfy the condition? (i.e., the number of points is not finite)

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# Using a different definition of norm

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