## Function

##### 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

AandBbe sets.fis said to be a function from setAto setBif and only if for each elementxofAthere is associated a uniquely determined elementf(x) ofB. The setAis called the domain of f and the elementsf(x) are called the values of f. The set of all values offis called the range off.

Notation:f:A-->Band read as f is a function fromAtoB

-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.

*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!)

(This is many-to-one relation. So, is a function too!)

*(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? ^^

Wednesday, March 04, 2009 5:05:00 AM

I never thought of this! ugh, i just finished my math course.. wish i knew bout this earlier.. this is much easier to remember.. haha

Wednesday, March 04, 2009 2:38:00 PM

yea.. actually it is much more easier to remember.. ^^