The possibility of approximating a continuous function on a compact subset ofthe real line by a feedforward single hidden layer neural network with asigmoidal activation function has been studied in many papers. Such networkscan approximate an arbitrary continuous function provided that an unlimitednumber of neurons in a hidden layer is permitted. In this paper, we considerconstructive approximation on any finite interval of $\mathbb{R}$ by neuralnetworks with only one neuron in the hidden layer. We construct algorithmicallya smooth, sigmoidal, almost monotone activation function $\sigma$ providingapproximation to an arbitrary continuous function within any degree ofaccuracy. This algorithm is implemented in a computer program, which computesthe value of $\sigma$ at any reasonable point of the real axis.
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