Quick Answer: What Is A Not Well Defined Set In Math?

What is not well defined set examples?

Example: “The collection of good students at MSUM” is not a set. All these questions indicate the statement is ambiguous, i.e., it is not clear which students are members of this collection, hence, the collection is not well – defined.

What is meant by well defined?

1: having clearly distinguishable limits, boundaries, or features a well – defined scar. 2: clearly stated or described well – defined policies.

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).

What is defined set in math?

A set in mathematics is a collection of well defined and distinct objects, considered as an object in its own right. The most basic properties are that a set “has” elements, and that two sets are equal (one and the same) if and only if every element of one is an element of the other.

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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 ).

What is the symbol of an empty set?

Empty Set: The empty set (or null set) is a set that has no members. Notation: The symbol ∅ is used to represent the empty set, { }. Note: { ∅ } does not symbolize the empty set; it represents a set that contains an empty set as an element and hence has a cardinality of one. Equal Sets.

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 is a well-defined problem?

Well – defined ( well -structured) problems are those that contain a clear specification of three elements of the problem space: the initial state (the problem situation), the set of operators (rules and strategies) to solve the problem, and the goal state (the solution).

What is the word for explaining something in a different way?

Some common synonyms of explain are elucidate, explicate, expound, and interpret. While all these words mean “to make something clear or understandable,” explain implies a making plain or intelligible what is not immediately obvious or entirely known.

How do you prove a function?

To prove a function, f: A → B is surjective, or onto, we must show f(A) = B. In other words, we must show the two sets, f(A) and B, are equal. We already know that f(A) ⊆ B if f is a well-defined function.

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What is a well defined limit?

A limit is well – defined if and only if both the left-sided limits and the right-sided limits exist and are finite. In this case, the right-sided limit exists and is 0, since as, then the function approaches 0. On the other hand, the left-sided limit does not exist.

What does Defined mean?

: to explain the meaning of (a word, phrase, etc.): to show or describe (someone or something) clearly and completely.: to show the shape, outline, or edge of (something) very clearly.

What is proper set example?

A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B. For example, if A={1,3,5} then B={1,5} is a proper subset of A.

What do you call a set with no elements?

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set ) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced.

How do you describe a set in words?

The Language of Sets A set is a collection of objects. Each of the objects in the set is an element. Two methods of describing sets are the roster method and set -builder notation. Example: B = {1, 2, 3, 4, 5} Example: C = {x| x ∈ N where x > 4} Example: Write B = {1, 4, 9, 16, …} in set builder notation.

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