I start by saying that it has taken over the word ‘ function ‘ of mathematics, and that the word in neither of these disciplines is synonymous with ‘ office ‘ or ‘ purpose ‘ or ‘ sentence ‘.It is actually one of the many examples of bad jargon in the sciences.
In high school you get to know math functions as graphs.This is a special case: every two-worthy relationship [MATHF (x, y) [/math linking a unique [ mathy [/math Of Type [ MATHB [/math to each [MATHX [/math of type [Matha [/math is a function [MATHF: A → B [/ Math ([mathf [/Math From [Matha [/Math to [MATHB [/math].The relationship ‘[MATHX [/math is the daughter of [Mathy [/math] is, for example, a function of women to women, although you cannot easily draw a chart there.
In structured programming languages, functions are often subroutines that can give a value back to them.A subroutine is a piece of code. Before you go there you save a few values in the memory for the subroutine to work with. However, a function also converts values so that the code that the function invokes can work with it.
What’s so different about mathematical functions and programming functions?
- Computers have a limited amount of memory to do their calculation and usually also a limited amount of time, energy etc.
That is to say, some programming functions are terminating due to lack of space or interrupted. Mathematical functions do not have this problem.
Mathematical functions do not have such an environment.
In Mathematics, we call this partial function.Programming functions do not make this distinction.
This allows us to define the following mathematical function: [MATHF (x, y) = Z [/math if [Mathx [/math written out as binary number is the code of a programming function [MATHG [/math , for which [MATHG (y) = Z [/math, For not negative integers [mathy [/math and [Mathz [/math.Additional condition here is that [MATHG [/math has all the limitation of a mathematical function, and for example must be total.If [MATHX [/math is not such a code, leave [MATHF (x, y) = 0 [/math.This [MATHF [/math seems to be a kind of universal function, which can do anything any other function can.However, there is a function [Mathh (x) = f (x, X) + 1 [/math and if [Mathh (x) = f (w, x) [/math for sure [MATHW [/math, then [Mathh (W) = f (w, w) = f (W, W) + 1 [/math.That is incondious. The mathematical function [mathh [/math is therefore not a programming function.
Mathematicians and Informaticians make mathematical models of programming functions, for example in denotational semantics (denotational semantics-Wikipedia). It adjusts the definition of mathematical functions to look more like a programming function.