On Definition of Holographic and Teaching in Mathematics

If a mathematical definition contains all the information of the defined item including properties etc, then such a definition is a holographic definition.From the holographic point of view, mathematical definition can be divided into two categories:holographic and non-holographic definition.For example, the definition of logarithm is holographic, so is the definition of trigonometric functions in the new teaching material by People’s Education Press.But none of the definitions of equation, quadratic equation and inequality is holographic.The holographic definition is good from the perspective of constructing the system of the mathematics science.Yet from the perspective of pedagogy, one will find it difficult to teach and learn a holographic definition.The teaching of holographic and non-holographic definitions differs significantly with emphasis placed on the former and deemphasis on the latter.