When proving Holder's inequality, why do we assume $\|x_i\|_p=1=\|y_i\|_q$, where $\frac{1}{p}+ \frac{1}{p}=1$.
$\|x_i\|_p=(\sum x_i^p)^{\frac{1}{p}}$.
Can it not be proven if the equality to unity condition is not taken?
When proving Holder's inequality, why do we assume $\|x_i\|_p=1=\|y_i\|_q$, where $\frac{1}{p}+ \frac{1}{p}=1$.
$\|x_i\|_p=(\sum x_i^p)^{\frac{1}{p}}$.
Can it not be proven if the equality to unity condition is not taken?