Final answer:
The truth of the statement 'when exists, it always equals f(a)' cannot be confirmed without additional context. It may be true if referring to the limit of a continuous function at a point, but clarity and precision are needed to determine its accuracy fully.
Step-by-step explanation:
The statement 'when exists, it always equals f(a)' is unclear and lacks sufficient context to determine its truth or falsehood definitively. Without knowing what 'it' refers to or what the function f represents, we can't make an accurate judgement on the statement. If 'it' is referring to the limit of a function as x approaches 'a', and if f is continuous at 'a', then it's true that the limit of f(x) as x approaches 'a' will equal f(a). However, if 'it' refers to something else, such as a conditionally defined function or an abstract mathematical concept, the statement's accuracy would depend on additional context.
In mathematics, it's crucial that statements are precise and accurately represent the concepts being discussed. For propositions to be true, they must correspond to the reality or defined mathematical structures they represent. The comparison of this statement to other mathematical concepts shows the importance of clarity in mathematical communication.