## The Triangle Inequality

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.

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.