What does it mean for a mapping to be well-defined?

3. The quickest explanation is that a “well-defined map” is a function. That is, the image of any given element in the domain, however you write or express it, is a single element in the range. This looks like showing one-to-oneness, but it’s only half of that.

How do you prove something is well-defined?

A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if f takes real numbers as input, and if f(0.5) does not equal f(1/2) then f is not well defined (and thus not a function).

How do you determine if a limit is well-defined?

A limit is well-defined if and only if both the left-sided limits and the right-sided limits exist and are finite.

1. In this case, the right-sided limit exists and is 0, since as , then the function approaches 0.
2. On the other hand, the left-sided limit does not exist.

What is another word for well-defined?

Words related to well-defined clear-cut, distinct, explicit, precise, straightforward, transparent, unambiguous, apparent, audible, comprehensible, graspable, intelligible, legible, lucent, lucid, obvious, plain, sharp, spelled out, unblurred.

Which is defined as a well defined group of objects?

Definition: A set is a well-defined collection of distinct objects. The objects of a set are called its elements. If a set has no elements, it is called the empty set and is denoted by ∅.

What are the example of well defined?

Well defined describes something that is clearly described and completely laid out. A yard with a fence in place is an example of a yard with a well defined boundary. The definition of well defined is physical features or attributes that are precise and outlined clearly.

What is well-defined example?

How do you say not well-defined?

ill-defined

1. murky.
2. unclear.
3. vague.
4. clouded.
5. dim.
6. indistinct.
7. obscured.

What is a well-defined map?

$\\begingroup$ The quickest explanation is that a “well-defined map” is a function. That is, the image of any given element in the domain, however you write or express it, is a single element in the range. This looks like showing one-to-oneness, but it’s only half of that.

How do you prove a set is well-defined?

To make the word “well-defined” appear, one reformulates this as follows: We want to define h: A / N → B. Let X ∈ A / N be an arbitrary element. Then there exists an x ∈ A such that X = x N. Set h ( X) := f ( x). This is well-defined, i.e. it does not depend on the choice of x.

How do you prove that a function is well defined?

To prove that a given function is well defined, you have to show that every input has one and only one output. The way we do this in our early math years is to graph the equation and show that it passes the “vertical line test.”

What is a well-defined mathematical object?

Checking that a mathematical object is well-defined is really just checking that it is defined: that the purported definition actually does unambiguously specify the object. It means “does not depend on choices made”.