msawicka wrote:
Hi Brent, can you explain why " If (something)² < 1, then it must be the case that -1 < something < 1"?
Let me try. It is because square, square root and absolute value go hand in hand. Let's say we have A^2=B, A can be any value, but B must be >=0 (i.e. non-negative, or positive inclusion of zero). We can rewrite it as A= + or - square root of B, which means any number under square root is >=0. In turn, if we are given square root of B = A, then B must be non-negative, so to make sure it satisfies this, we absolute value B => if we square both side, we get absolute value of B=A^2. In case of inequality, we have absolute value of B < A^2. And we have our familiar inequality: absolute value of B < A^2 <=> -A^2 < B < A^2.