- #1

- 10

- 0

**1.**

the p-norm for a vector x in R^n is defined usually:

|| x ||_p = (x_1^p + x_2^p + ... + x_n^p)^{1/p}

the question is to verify:

|| x ||_p <= || x ||_{p-1}

the p-norm for a vector x in R^n is defined usually:

|| x ||_p = (x_1^p + x_2^p + ... + x_n^p)^{1/p}

the question is to verify:

|| x ||_p <= || x ||_{p-1}

## Homework Equations

I guess even more generally p-norm is a decreasing function in p for "any" x?

## The Attempt at a Solution

Neither Cauchy, nor the more general Holder doesn't seem to apply.