Continuity: Meaning, Notation, and Example
At a point, the function value exists and equals the limit there.
Definition and meaning
Continuity joins existence of f(a), existence of the nearby limit, and equality between them.
The term continuity names a precise mathematical idea, not merely a visual pattern. Read its notation as a statement with hypotheses, quantities, and a conclusion.
Notation
Read every symbol with its domain and hypotheses; notation compresses an argument but does not remove its conditions.
Worked example
Identify the quantities in the notation, state the relevant hypothesis, and explain what conclusion the continuity statement permits.
Common confusion
Do not treat continuity as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.