Changes

=== Metric Spaces ===

=== Metric Spaces ===

Let <math>X\,</math> and <math>Y\,</math> be to [[metric space]]s, and <math>f: X \rightarrow Y</math> a function between these two sets. Then <math>f\,</math> is ''continuous'' in <math>x_0 \in X</math> if for all <math>\epsilon > 0\,</math> there is a <math>\delta > 0\,</math> such that for all <math>x\,</math> with

Let <math>X\,</math> and <math>Y\,</math> be two [[metric space]]s, and <math>f: X \rightarrow Y</math> a function between these two sets. Then <math>f\,</math> is ''continuous'' in <math>x_0 \in X</math> if for all <math>\epsilon > 0\,</math> there is a <math>\delta > 0\,</math> such that for all <math>x\,</math> with

::<math> |x - x_0| < \delta\,</math>

::<math> |x - x_0| < \delta\,</math>