Point of Inflection Definition

Question

What is the definition of Point of Inflection.

1. Some books say the point where the curve changes its concavity is called point of inflection
2. Some authors say the point where tangent exist and the concavity changes is called point of inflection

So can a sharp corner where concavity changes be a point of inflection Eg F(x)=$$ |x^2 - 4| $$ can we say x = 2 and -2 are point of inflection. (By first definition they are point of inflections but by second they are not)

Similarly, if concavity changes around a discontinuous point, will that be counted as point of inflection.

Thanx