Can someone solve this problem?
PROVE: For any real numbers a and b ||a|-|b||≤ |a-b|
You need to know the triangular inequality.
$\displaystyle |a| = |a - b + b|$
$\displaystyle = |(a - b) + b|$
$\displaystyle \leq |a - b| + |b|$.
Since $\displaystyle |a| \leq |a - b| + |b|$
$\displaystyle |a| - |b| \leq |a - b|$.
If we take the modulus of both sides, we have
$\displaystyle \left||a| - |b|\right| \leq \left||a - b|\right|$
$\displaystyle \left||a| - |b|\right| \leq |a - b|$.