Mark44
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bugatti79 said:##x+y=(x_1+y_1, x_2+y_2)##
## \| x+y\|_{\#}= \| |x1|+|y1|, 2|x2|+2|y2| \|_{\#} ##...?
Did you use the definition?
bugatti79 said:(i) || ||_#: R^2 defined by ||x||_#=|x_1|+2|x_2|
Doesn't look like it to me.