The triangle inequality comes in two versions.
Theorem
If
then
Proof:
-
is proved.
For part 2. note that
so that
by part 1.
so that
Similarly
Since
we have
so that 2. follows.
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The triangle inequality comes in two versions.
Theorem
Ifthen
Proof:
is proved.
For part 2. note that
so thatby part 1.
so that
Similarly
Sincewe haveso that 2. follows.