Editing Continuous function (section)

===Directional Continuity===
<div style="float:right;">
<gallery>Image:Right-continuous.svg|A right-continuous function
Image:Left-continuous.svg|A left-continuous function</gallery></div>
Discontinuous functions may be discontinuous in a restricted way, giving rise to the concept of directional continuity (or right and left continuous functions) and [[semi-continuity]]. Roughly speaking, a function is {{em|right-continuous}} if no jump occurs when the limit point is approached from the right. Formally, ''f'' is said to be right-continuous at the point ''c'' if the following holds: For any number <math>\varepsilon > 0</math> however small, there exists some number <math>\delta > 0</math> such that for all ''x'' in the domain with <math>c < x < c + \delta,</math> the value of <math>f(x)</math> will satisfy
<math display="block">|f(x) - f(c)| < \varepsilon.</math>

This is the same condition as continuous functions, except it is required to hold for ''x'' strictly larger than ''c'' only. Requiring it instead for all ''x'' with <math>c - \delta < x < c</math> yields the notion of {{em|left-continuous}} functions. A function is continuous if and only if it is both right-continuous and left-continuous.