Suppose we have a function formula_16 which takes two real number (formula_17) arguments and outputs real numbers, and it is defined by formula_18. Currying translates this into a function formula_19 which takes a single real argument and outputs functions from formula_17 to formula_17. In symbols, formula_22, where formula_23denotes the set of all functions that take a single real argument and produce real outputs. For every real number formula_24, define the function formula_25 by formula_26, and then define the function formula_22 by formula_28. So for instance, formula_29 is the function that sends its real argument formula_30 to the output formula_31, or formula_32. We see that in general