Continuity

In calculus and related fields, continuity is the property of a function roughly meaning "the graph can be drawn without lifting the pen."

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• a function $f:ℝ\to ℝ$ is continuous at $a$ if $fa$ is defined and ${\lim }_{x\to a}fx=fa$.

Definition

A function $f$ is continuous at an input value $a$ if

1. $fa$ is defined,

2. ${\lim }_{x\to a}fx$ exists,

3. and ${\lim }_{x\to a}fx=fa$.