trobinson41
New member
- Joined
- Dec 29, 2014
- Messages
- 2
Let C[a,b] be the set of all real-values functions that are continuous on the closed interval [a,b]. According to my book the following does NOT define a norm:
|| f || = |f(a)| + |f(b)|
The book does not explain why. I'm guessing that it doesn't satisfy the triangle inequality, but I can't think of a counterexample.
A norm has to satisfy the following conditions:
Let v, w be members of a vector space V.
1. || v || >= 0 and is equal to 0 if and only if v = 0.
2. || av || = |a| || v || for any scalar a.
3. || v + w || <= || v || + || w ||
Thanks.
|| f || = |f(a)| + |f(b)|
The book does not explain why. I'm guessing that it doesn't satisfy the triangle inequality, but I can't think of a counterexample.
A norm has to satisfy the following conditions:
Let v, w be members of a vector space V.
1. || v || >= 0 and is equal to 0 if and only if v = 0.
2. || av || = |a| || v || for any scalar a.
3. || v + w || <= || v || + || w ||
Thanks.