I don't quite understand what you're doing here, why are you choosing this ? Are you secretly plugging this in because it's the max, and you just omitted this? Give us more words, explaining your choices etc. and then we can help you decide of what you did is correct. A quick check: you should be proving that for every there exists such that where is the infinity norm. This 'looks' like what you're doing, but please fill in more holes.