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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}

2. Relevant equations

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

3. The attempt at a solution

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

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: ? p-norm <= (p-1)norm <= <= 2-norm <= 1-norm?

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