Machine Learning, Data Science, Artificial Intelligence.
Informally, the function 𝑓 is continuous at a point 𝑎∈𝐴 if for every open ball around 𝑓(𝑎) in 𝐶, there exists a corresponding open ball around a in A such that the image under f of this latter ball is contained within the open ball around 𝑓(𝑎). Formally, a function f is continuous at a point 𝑎 if,