- #1
Bipolarity
- 776
- 2
The following inequality can easily be proved on ##ℝ## :
## ||x|-|y|| \leq |x-y| ##
I was wondering if it extends to arbitrary normed linear spaces, since I can't seem to prove it using the axioms for linear spaces. (I can however, prove it using the definition of the norm on ##ℝ## by using casework).
Suggestions? Hints?
BiP
## ||x|-|y|| \leq |x-y| ##
I was wondering if it extends to arbitrary normed linear spaces, since I can't seem to prove it using the axioms for linear spaces. (I can however, prove it using the definition of the norm on ##ℝ## by using casework).
Suggestions? Hints?
BiP