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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]
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 · The term well-defined (as oppsed to simply defined) is typically used when a definition seemingly depends on a choice, but in the end does not. In most (but not all) cases, this applies to the definition of a function $f\colon A\to B$ in terms of two given functions $g\colon C\to A$ and $h\colon C\to B$: For $a\in A$ we want to define $f(a)$ by ...
4 ημέρες πριν · 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 abc (the product) is well-defined if a, b, and c are integers.
15 Ιαν 2021 · A function $f: A \to B$ is well defined if for every $x \in A$, $f(x)$ is equal to a single value in $B$. So if $f(x)$ could equal two different values in $B$, then it is not well defined. Or if $f(x)$ is not equal to a value in the set $B$, then it is not well defined.
In mathematical jargon that developed long before our current understanding of functions as sets of pairs, we refer to a relation whose being a function requires a proof as well-defined. Instead of defining a relation and checking its “functionality”, we just write it down as if we knew it was a function and check whether everything makes ...
A concept or term is considered well-defined when its meaning is clear, precise, and unambiguous, allowing it to be universally understood in a mathematical context. This clarity is crucial for establishing the rules or operations within recursive definitions and ensuring that structural induction can be applied consistently.
