- #1

infinitylord

- 34

- 1

## Homework Statement

I have a homework problem in honors calculus III that I'm having a little trouble with. Given these three qualities of norms in R

^{n}:

1) f(v)[itex]\geq[/itex]0, with equality iff v=0

2) f(av)=|a|f(v) for any scalar a

3) f(v+w) [itex]\leq[/itex] f(v)+f(w)

we were given a set of 3 functions and told that 2 were norms and 1 was not a norm. I very easily classified that f(v1,...,vn)=|v1|+...+|vn| was a norm using these three properties. the two left were g(v1,...vn) = min(|v1|,...,|vn|) and h(v1,...vn) = max(|v1|,...,|vn|). I determined through some research that the maximum function was a norm and the minimum function was not. But I don't know why that is. I tried using the triangle inequality 3) to prove this, but I came up with the inequality being true for both the max and min. I'm really not sure what to do from here as I believe that both of the first 2 properties of norms work for the max and min. I was reliant on the triangle inequality being the counterexample I needed for the minimum function. If someone could help me out I'd greatly appreciate it!

Last edited: