It is said taht function is the central idea in the story of math. In what why and haw. explain ???

Question

math , functions ,

Answer 1

There some good ideas suggested by my predecessors, however let us develop it a bit slower.

The central idea is that a function is a one to one relationship a variable or a set of variables. That means that… we will get to that in a moment.

Consider a couple of examples:

1.Relationship to an independent variable
y=x is another straight line with a 45 degree slope passing through (0.0) point and running between x and y axis

2.Relationship to several independent variables
y=3x+2z so y=f(x, z) and it is a straight line again.

Using example #1 we can call y a function of x of f(x) and x is its independent variable (and keep in mind that nothing prevents as from saying that x is a function of y of f(y), but is best to keep at least one independent). In example #2 we have two independent variables namely x and z.

Note that for every x there is a unique value of y or in the second example for every (x, z) pair there was a unique value for y.

That means that the relationship is binary that is for every x there is a unique y. But what about y=3x+2z, don’t we have a ternary relationship since we have (x, y and z)? Not really since y=3x+2z represents a three dimensional superposition of two functions y=3x and y=2z. The binary relationship still holds.

In short a function represents a relationship between variables and this why it is a central idea. A function is a mathematical model of physical phenomena such a relationship od force and acceleration

F=ma

Answer 2

Function...

http://en.wikipedia.org/wiki/Function_%28mathematics%29 ...

hope this will guide you to it, it needs your elaborate and specific question to answer it.

But for curiosity, the result is the central idea in the story of math. Problems is the main central focus to be solved.

Answer 3

yes, it relates mathematical objects between them.
for example you want to study the set A and find a nice function to B and you know lots of things about B , then you can find lots of information about A