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This is a place to ask questions about math terminology, and to post links to other resources out on the web.
2006-09-04 16:13:19
Function Definition

What is 'your' definition of a mathematical function? No links please.

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.

2006-09-05 00:38:19
Re: Function Definition

In your definition, is 'relation' a set of ordered pairs?

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.

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.

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.

2006-09-05 10:21:34
Re: Function Definition

But on the other hand, I don't usually consider the ordered pairs aspect.

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.

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.

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