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Boolean functions:
 Every boolean function can be represented by network with single hidden
layer
 but might require exponential (in number of inputs) hidden units
Continuous functions:

Every bounded continuous function can be approximated with arbitrarily small
error, by network with one hidden layer [Cybenko 1989; Hornik et al. 1989]

Any function can be approximated to arbitrary accuracy by a network with two
hidden layers [Cybenko 1988].