Bractals
2006-09-04 16:13:19 |
Function Definition
What is 'your' definition of a mathematical function? No links please. |
Charlie
2006-09-04 22:40:04 |
Re: Function Definition
A relation that assigns a unique number to any number in a particular range. The range need not be continuous. |
Bractals
2006-09-05 00:38:19 |
Re: Function Definition
In your definition, is 'relation' a set of ordered pairs? |
brianjn
2006-09-05 02:07:38 |
Re: Function Definition
This is a 'philosophy' survey, right?
You could get ample definitions from wherever.
How we personally view this matter? That is the question, I believe.
Tough! But ...
I view a function as a set of criteria (may be a singular entity) which defines the behaviour of some phenomenal occurrence.
Clarity:
I think I view this concept in two lights.
1. I have a tendency to see a function as a formula, I change values within the structure and so get a different entity.
2. The function, while being a formula, can have limitations placed upon that behaviour.
OK. With those thoughts in mind I redefine:
A function as a set of criteria (may be a singular entity) which defines the behaviour of some phenomenal occurrence within certain limitations. |
Charlie
2006-09-05 10:17:42 |
Re: Function Definition
Yes, a relation could be considered as a set of ordered pairs, which usually, but not always is infinite in cardinality, and the constraint that the second member (by convention) is called the dependent variable and is unique for any given first member, within the set of ordered pairs. |
Charlie
2006-09-05 10:21:34 |
Re: Function Definition
But on the other hand, I don't usually consider the ordered pairs aspect. |
Jer
2006-09-05 11:45:14 |
Re: Function Definition
'my' definition? How about:
A relation between sets which for any allowable input gives a uniquely determined output.
The sets are usually numbers and the allowable inputs are called the range. |
Bractals
2006-09-05 16:58:02 |
Re: Function Definition
What do you think of the following definition.
A function, say f, from a set A to a set B, denoted by f:A-->B, is a subset of the Cartesian product AxB such that for all a in A, |f^({a}xB)| = 1.
Where ^ denotes set intersection.
f is one-to-one (injective) if for all b in B, |f^(Ax{b})| <= 1.
f is onto (surjective) if for all b in B, |f^(Ax{b})| >= 1.
f is one-to-one and onto (bijective) if for all b in B, |f^(Ax{b})| = 1.
|
