Question 3.6: If xn → x then |xn| → |x| .
If x_{n} → x then |x_{n}| → |x| .
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We know that
0 ≤ ||x_{n}| − |x|| ≤ |x_{n} − x| for all n ∈ \mathbb{N}.
Since x_{n} → x implies |x_{n} − x| → 0, it follows from Theorem 3.6 that |x_{n}| − |x| → 0, or |x_{n}| → |x| .
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