Consider a norm on Rn.
there are two vectors x,y in Rn
x=(x1,x2,x3,...,xn)
y=(y1,y2,...,yn)
if, y1>x1,
y2>x2,
y3>x3,
.
.
.
yn>xn
.
is it true that norm : ||y||>= ||x|| for any norm on Rn?
yes, i know what the norm is defined as. i asked you to compare with (we can do this since we were given comparisons component wise).
anyway, just make a counter example, it shouldn't be hard. consider vectors in given by
and
do those vectors satisfy the conditions given? is ?