Abstract
This chapter discusses functions and their limitations. If to any real number corresponds a certain number, then a function is defined over the set of real numbers. Not every function is defined over the whole set of real numbers. Projecting the graph of a function on the x-axis one can obtain the set of arguments of the function. Projecting it on the y-axis we obtain the set of values of the function. Among the sets lying on the plane, the graphs of functions are characterized by the property that no straight line parallel to the y-axis contains two points of the set. Functions of one variable in distinction to functions of two and more variables and by a function of one variable, a number corresponds to any real number (belonging to the set of arguments), by a function of two variables, the value corresponds to the values of an ordered pair.
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