A World of Fours

The expressions that employ as digits only three 4s and the conventional mathematical symbols are endlessly varied.

4 x 4!
4
4 x 4 4
4 x 4 x 4!!

A little research shows that one can represent most values of the positive integers, assuming a resourceful use of arithmetic operations.But is it possible to construct a universal formula adaptable to the expression of any positive integer n? If necessary, one can use an unlimited number of operations.

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