A Decision Method for Elementary Algebra and Geometry

By a decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K; by a decision problem for a class K we mean the problem of finding a decision method for K. A decision method must be like a recipe, which tells one what to do at each steps so that no intelligence is required to follow it; and the method can be applied by anyone so long as he is able to read and follow directions.