For any x=(x1,....,xn), let us try to define a norm two ways. Consider
(a) ||X||1=summation |Xi| from i=1 to n
(b) ||X||b=summation |xi-xj| from i,j=1 to n
Does either one of these formulas define a norm? If yes, show that all three axioms of norm hold. If no, demonstrate which axiom fails.
Summations are investigated as to whether they define norms. The solution is detailed and well presented.