Definition of Continuity

The definition of continuity used by mathematicians today was developed by Karl Weierstrass of Ostenfelde, Westphalia (now Germany). Karl role in math history is important: he introduce a rigorous analysis of mathematical concepts that leads the way for later advancements.

Continuity

A function f(x) is continuous at x = x₀ if, for an arbitrarily small &epsilon > 0, there exists δ > 0 such that |x - x₀| < δ implies that |f(x) - f(x₀)| < δ.

Examples of the Definition of Continuity