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10 Μαΐ 2023 · We say the function (or, more precisely, the specification of the function) is 'well-defined' if it does. That is, $f : A \to B$ is well-defined if for each $a \in A$ there is a unique $b \in B$ with $f(a)=b$.
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.
1 Φεβ 2016 · If $f(x)=f(y)$ whenever $x$ and $y$ belong to the same equivalence class, then we say that $f$ is well-defined on $X/E$, which intuitively means that it depends only on the class. More rigorously, what happens is that in this case we can ("well") define a new function $f':X/E\to Y$, as $f'([x])=f(x)$.
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]
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.
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.
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.
