Hi, I have a question about taylor polynomials. https://wikimedia.org/api/rest_v1/media/math/render/svg/09523585d1633ee9c48750c11b60d82c82b315bf I was looking for proof that why every lagrange remainder is decreasing as the order of lagnrange remainder increases. so on wikipedia, it says, for a function to be an analytic function, x must be in the neighborhood of x0. What does this neighborhood mean by? should that be r=|x-x0|<1? then everything makes sense.