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An function is often called an map or a mapping. The set is X is called the domain and denoted by dom(f), and the set Y is called the codomain and denoted by cod(f). When we know what these two sets are and the two conditions are satisfied, we say that f is a well defined function.
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. [1]
5 ημέρες πριν · Well-Defined. An expression is called "well-defined" (or "unambiguous") if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be well-defined or to be ambiguous. For example, the expression (the product) is well-defined if , , and are integers.
Mathematicians define mathematical objects, and if the definition is syntactically correct, the objects are always “well-defined”. What may happen, however, is that the defined object is not a function.
The only thing that is really important is the requirement that the function be well-defined, and by “well-defined,” we mean that each object in the function’s domain is paired with one and only one object in its range.
Well-defined means, it must be absolutely clear that which object belongs to the set and which does not. For example: ‘The collection of positive numbers less than 10’ is a set, because, given any numbers, we can always find out whether that number belongs to the collection or not.
17 Αυγ 2020 · In order to make a ⊙ b have a valid answer (let’s say, a ⊙ b = c is a valid construction), we need to show that ⊙ is a well-defined operation. For any well-defined operations, if I take a value...
