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Today, I will demonstrate the use of the intermediate value theorem to prove that a function has a fixed point. If we have a function f that is continuous from 0 to 1, then there exists a specific point, say 1/2, where applying f results in no change. This fixed point x naught lies within the interval 0, 1, satisfying f(x naught) = x naught. Geometrically, this implies that the function must intersect the line y = x at some point.