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What is a not well-defined set in math?

What is a not well-defined set in math?

In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. A function that is not well defined is not the same as a function that is undefined.

What are well-defined collections and sets?

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 ∅. Note: ∅ is not the same as 0.

What is a well-defined function?

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 will you define well-defined set and universal set?

A universal set (usually denoted by U) is a set which has elements of all the related sets, without any repetition of elements. Say if A and B are two sets, such as A = {1,2,3} and B = {1,a,b,c}, then the universal set associated with these two sets is given by U = {1,2,3,a,b,c}.

How do you know if the set is well-defined?

A set is well-defined if there is no ambiguity as to whether or not an object belongs to it, i.e., a set is defined so that we can always tell what is and what is not a member of the set. Example: C = {red, blue, yellow, green, purple} is well-defined since it is clear what is in the set.

What is another word for well-defined?

precise, unambiguous, straightforward, distinct, clear-cut, explicit, transparent, apparent, audible, comprehensible, intelligible, legible, lucid, obvious, plain, sharp, understandable, lucent, graspable, spelled out.

What are the examples of well-defined sets?

Why set is well-defined?

How do you show well-defined?

So to say that something is well-defined is to say that all three things are true….When we write f:X→Y we say three things:

  1. f⊆X×Y.
  2. The domain of f is X.
  3. Whenever ⟨x,y1⟩,⟨x,y2⟩∈f then y1=y2. In this case whenever ⟨x,y⟩∈f we denote y by f(x).

How empty set is well defined?

Thus, if an object does not exist then it is a well defined object for an empty set. For example, Odd numbers which are divisible by 2 are well defined objects for an empty set. A hen with horns is also a well defined object for an empty set.

What are the different kinds of set?

Types of a Set

  • Finite Set. A set which contains a definite number of elements is called a finite set.
  • Infinite Set. A set which contains infinite number of elements is called an infinite set.
  • Subset.
  • Proper Subset.
  • Universal Set.
  • Empty Set or Null Set.
  • Singleton Set or Unit Set.
  • Equal Set.

Which is an example of a well defined set?

In mathematics, a well-defined set clearly indicates what is a member of the set and what is not. For example, a set that is identified as “the set of even whole numbers between 1 and 11” is a well-defined set because it is possible to identify the exact members of the set: 2, 4, 6, 8 and 10.

Is the set of US presidents a well defined set?

The set of U.S. presidents is a well-defined set because its contents, the presidents. can be named. The set of the three best movies is not a well—defined set because the word best is interpreted differently by different people.

Is the term most dangerous a well defined set?

(iv) The term most dangerous is not a well—defined term. An animal may be most dangerous for one person and may not be for the other. So, it is not well—defined. Hence, it is not a set.

Which is a well defined set in mathlibra?

‘The rivers of lndia’ is a Well—defined collection. Since, We can say that the river Nile does not belong to this collection. On the other hand, the river Ganga does belong to this collection. A group of intelligent students. A group of students scoring more than 95% marks of your school.