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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 $f(a)=b$.
5 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 (the product) is well-defined if , , and are integers.
Given an equivalence relation on a set $A$ and function $f:A \rightarrow B$, saying that $f$ is well-defined, means that $f^{\sim} : A/ \sim \rightarrow B$, $f^{\sim}([x])=f(x)$, define a function.This happen if, $ x\sim y$ imply $f(x)=f(y)$ ($f$ pass to the quotient).
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.
What does "Well Defined" Mean? Sooner or later you will have to prove that something is "well defined". So what does this mean? Let's look at an example. Example: Congruence Arithmetic For integers a and b and a positive integer m, we say that a is congruent to b modulo m, written a = b mod(m), if a - b is evenly divisble by m. Another way of ...
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 ...
