Let us look at examples for several values of n:
n = 1: Take y = (
6).
Then ||y|| = 361/2 = 6.
Thus, when n = 1, ||y|| is just the absolute value of the single coordinate of y.
n = 2: Take y = (3, 4).
Then ||y|| = (9 + 16)1/2 = 5,
which is the distance from the point (3, 4) to the origin in the plane.
n = 4: Take y = (3, 1, 2, 2).
Then ||y|| = (9 + 1 + 4 +4)1/2 = 181/2,
which is the distance from the point (3, 1, 2, 2) to the origin in Euclidean 4-space.
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