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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]
When we know what these two sets are and the two conditions are satisfied, we say that $f$ is a well defined function. Condition i) makes sure that each element in $X$ is related to some element of $Y$, while condition ii) makes sure that no element in $X$ is related to more than one element of $Y$.
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 $f(a)=b$.
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.
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.
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.
18 Οκτ 2021 · The discussion of modular arithmetic ignored a very important point: the operations of addition, subtraction, and multiplication need to be well-defined. That is, if ¯ a1 = ¯ a2 and ¯ b1 = ¯ b2, then we need to know that. ¯ a1 + n ¯ b1 = ¯ a2 +n ¯ b2, ¯ a1 −n ¯ b1 = ¯ a2 − n ¯ b2, and. ¯ a1 ×n ¯ b1 = ¯ a2 ×n ¯ b2.
