# Thread: Definiton required

1. ## Definiton required

What does well defined mean?

For example, a tangent line is well defined.

The closest definition I've come to is a function that refers to itself. But in my eyes that's not good enough because well defined is used so loosely in what I read.

2. ## Re: Definiton required

Originally Posted by PilgrimsPath
What does well defined mean?
For example, a tangent line is well defined.
The closest definition I've come to is a function that refers to itself. But in my eyes that's not good enough because well defined is used so loosely in what I read.
You can find a reasonably general discussion: SEE HERE Also SEE HERE

In a set theory/foundations course there is a much more precise formulation. Basically there is a set of axioms & definitions. There must exist a model for those statements. Then a concept is well-defined provided that it can be uniquely modeled.

3. ## Re: Definiton required

I get it! Well-defined; and ill-defined!

Sorry for you having to dumb me down with Wiki. I'm so used to referring to a math's dictionary it surprised me why on earth this is not in there. Supposedly my dictionary is concise. I beg to differ.

4. ## Re: Definiton required

Originally Posted by PilgrimsPath
Sorry for you having to dumb me down with Wiki. I'm so used to referring to a math's dictionary it surprised me why on earth this is not in there. Supposedly my dictionary is concise. I beg to differ.
I have no idea what any of your response means. I had no intention of dumbing anything down. Either one understands the simple idea of the correspondence theory of truth. That is the assumption taken by Wiki, no dumding down there. Or have you studied model theory on the level of say Jerome Keisler You can find free down-loads HERE.

You asked really a straightforward question. Having no idea as to your level of study, I gave you two possible levels of answers based upon the way you stated the question. Actually your stated the question in a very naive way. My reply was simply an attempt to give a reasonable answer to what you posted.

5. ## Re: Definiton required

Eh, what are you on about old man?

The point I made in my statement, "dumbed down by Wiki" was that I consulted a below par maths dictionary thinking a definition of well-defined would be contained with in; this was not so. I then turned to MHF and got dumbed down with Wiki; as in did this resource not cross your mind!?

Apologies for any confusion. Presumably, you're not British.