There is a noted isomorphism between continued fractions and nested radicals, specifically illustrated by the equation y = √(x + √(x + √(x + ...))). The derived quadratic equation y² - y - x = 0 leads to the solution y = (1 ± √(1 + 4x))/2, with the positive branch y = (1 + √(1 + 4x))/2 for x > 0 and y > 0. However, there is a concern regarding the initial condition, as substituting x = 0 yields y = 0, which raises questions about the formula's validity at x = 1. The discussion highlights potential issues with the definition and continuity of the formula. Overall, the relationship between continued fractions and nested radicals invites further exploration and clarification.