- #1
Oxymoron
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I am working through some exercises and need some help on a couple of questions.
1. Show that in any inner product space [tex]X[/tex] that
[tex]B[x;r] = x+rB[X] := \{x+ry\,:\, y\in B[X]\}[/tex]
where [tex]B[X][/tex] is the closed unit ball.
2. Show that the closed unit ball is convex.
I have thought about these questions, and I can picture them. However, I can't begin to prove them. Can anyone get me started? I only need pointers.
Thanks.
1. Show that in any inner product space [tex]X[/tex] that
[tex]B[x;r] = x+rB[X] := \{x+ry\,:\, y\in B[X]\}[/tex]
where [tex]B[X][/tex] is the closed unit ball.
2. Show that the closed unit ball is convex.
I have thought about these questions, and I can picture them. However, I can't begin to prove them. Can anyone get me started? I only need pointers.
Thanks.