Normed Vector Space: Proving L1, L2, and L-Infinity are Norms

[CarmineCortez]

Homework Statement

I have to show that l¹, l² and l^infinity are norms

The Attempt at a Solution

Do you just go through the conditions for norm spaces ie:
1. ||x||>0, ||x|| = 0 iff x = 0
2.triangle inequality
3.||cx|| < |c|||x||

if the space satisfies these conditions it is a norm??

 

[dirk_mec1]

Homework Statement

Do you just go through the conditions for norm spaces ie:

Yes, that's right.

 

[rochfor1]

You do just verify the points of the definition of a norm, but your 3rd point is a bit, off i believe there should be equality.