For any real number \(x\), the absolute value of \(x\), written \(\left| x \right|\), is define to be \(x\) if \(x>0\) and \(-x\) if \(x \leq 0\). What is \(\left| 3 \right|\), \(\left| -4.3 \right|\) and \(\left| 0 \right|\)?
Prove that for any real number \(x\), \(x \leq \left| x \right|\) and \(0 \leq \left| x \right|\). Then prove that for any real numbers \(x,y\), the triangle inequality holds: \(\left| x+y \right| \leq \left| x \right|+\left| y \right|\).