continuity definition

Continuity, in mathematical terms, means that a function has no abrupt jumps or breaks. More precisely, if you imagine drawing the function without lifting your pen, it would be possible to do so smoothly, without sudden jumps or gaps. At any point within its domain, a function is continuous if the output value there is exactly what you'd expect by approaching from nearby points. This ensures the function behaves smoothly and predictably, with no unexpected surprises. In essence, continuity signifies that small changes in input lead to small changes in output, maintaining a seamless connection across its domain.