Continuous Function : Original Concept : Real Analysis : B.sc.Mathematics #realanalysis #continuousfunction
For a video explanation, click here 👉 https://youtu.be/YKNZT-lU7_w Here in this page , i completely explained the original meaning of a continuous function at a point on the domain in detail. CONTINUOUS FUNCTION : Definition : A real valued function f : X → R is said to be continuous at a point a in X if " for a given 𝞊 > 0 ∃ 𝝳 > 0 such that | f (x) - f(a) | < 𝞊 whenever | x-a | < 𝝳 . now here is the explanation of the above definition. Before going to the definition, we should learn two things. 1. | x - y | means the distance between x and y. 2 . | x-a | < r means x lies in circle with center a and radius r. Note : Here circle means the neighbourhood. For convinince or easily understand, here iam considering a neighbourhood in the real line as a circle. ...