Example of Seq of functions cgs to 0 with metric d1 | L9 | TYBSc Maths | Completeness ‪@ranjankhatu‬

hi everyone in this video we are going to discuss this very small example so we have x x is defined as C Clos interval 01 that means it is a set of all continuous functions this is y axis this is x-axis okay we have a Clos interval 01 here right so you can easily see this is a continuous function defined on Clos interval 01 this is also a continuous function this is also a continuous function getting on defined on closed interval 01 so X is a set of all such functions FN of T is one of it it is defined in this way actually it is a sequence of function and our Target is to prove this FN of T converges to zero right with this matric the matric is defined in different way it's 0 to 1 mod f of T minus G of T DT so first of all tell me when we say sequence x n converges to X when we say let us draw the diagram and try to understand the meaning of it this is first point of a sequence first term second term third term if all term s of a sequence are moving towards a single point then we say the sequence converges to X points are moving towards X that means distance between each point and X is moving towards zero that means suppose if you take X5 here distance between X5 and X okay X7 and X X9 and X so distance is reducing and it is moving towards zero then we say the sequence is convergent and converges to X same logic I'm going to use here here also our main focus on distance of distance between FN and zero so let us find consider I'm going to find the distance that means with this mric obviously D1 FN and zero I'm going to find the distance right D1 definition is given here let us follow 0 to 1 mod f f of T the first function G of T that means