Saturday, February 28, 2009

Weeks ago, while listening in the lectures, Real Analysis lecture, to be more specific, the lecturer taught us this --> Function.

Students in science stream will be exposed to function when they're in Form 4. Well, this should be the first topic of the add maths if I'm not mistaken. ^^

So, function. The definition of function is...

Let A and B be sets. f is said to be a function from set A to set B if and only if for each element x of A there is associated a uniquely determined element f(x) of B. The set A is called the domain of f and the elements f(x) are called the values of f. The set of all values of f is called the range of f.

Notation: f : A --> B and read as f is a function from A to B

-From Real Analysis's lecture notes-

Which means that, a function can be called a function when the f : A --> B are injective (one-one), subjective (onto) or bijective (both injective and subjective). In a simple form, function is a many-to-one and one-to-one relation. A one-to-many relation is not a function.

Some may think is hard to remember. But no worries. Thanks to my friend who came out with an idea on how to memorise it.

Let A (domain) as MEN, and B (range) as WOMEN

Men cannot live without women, but women can live without men.
(This is one-one relation. So, it's a function.)

Two men can have the same woman on the same time...
(This is many-to-one relation. So, is a function too!)

.. but one man cannot have more than one woman at the same time.
(This is not a function cos is a one-to-many relation)

So, can u remember what relation should the function be in order to call a function? ^^

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