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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.
- "Well defined" function - What does it mean? - Mathematics Stack Exchange
We say the function (or, more precisely, the specification...
- soft question - Definition of "well defined" in mathematics ...
Let $f(x)$ be a function defined on $\mathbb R^+$ such that...
- "Well defined" function - What does it mean? - Mathematics Stack Exchange
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 $f(a)=b$.
1 Φεβ 2016 · Let $f(x)$ be a function defined on $\mathbb R^+$ such that $f(x)>0$ and $(f(x))^2=x$, then $f$ is well defined. This means that the statement about $f$ can be taken as a definition, what it formally means is that there exists exactly one such function (and of course it's the square root).
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.
