Evaluation operator

This page is about 大, the chinese character, and its mathematical application as evaluation operator.

The symbol

大 is a chinese character pronounced "da" (mandarin) or "dai" (cantonese). It symbolizes a man spreading out his legs and arms to make himself look big. Thus, it translates to: big, huge, massive or great.

Mathematical definition

大 is used as the mathematical symbol for the evaluation operator.
It is applied to functions and inserts values for unbound variables.
This operator simply replaces every instance of one variable with a numeric value or a mathematical expression.

In case there are contextually defined initial values for the free parameters they may be implicitely assumed.

Example of application

The evaluation operator is applied in mathematics for the expression of sequential processes, computer programs and algorithms.

Consider for instance the following simple algorithm for the computation of the Mandelbrot set.
It clearly represents a mathematical function in , but is difficult to express in explicit or closed form.

FOR i := 1 TO 100 x := x^2 - 1 END PRINT SGN(ABS(x)-10) Using 大, the function can be written in explicit form and integrated in mathematical notation.

The mathematical notation uses the operator power the express the repeated operator application. Individual 大's are placed in the same order as in the computational procedure.
Programming constructs like the conditional branch can be expressed by the decision operator.

Alternative notation

An alternative and very common notation for the same mathematical concept is expressed by the bar operator.
In contrast to all other mathematical operators it is applied from the right hand side and is notationally difficult to raise to a power.