Infix notation is the notation commonly used in arithmetical and logical formulae and statements. Numerical marking is the manner of denoting the arithmetical values of contour lines. The remaining axioms define the arithmetical properties of the natural numbers. In this book, Thabit deals with arithmetical operations applied to ratios of geometrical quantities. For instance, the level formula 1 of the arithmetical hierarchy classifies computable, partial functions. Electrical machines will be the advancement of arithmetical computation. The most well known are arithmetical reducibility and hyperarithmetical reducibility. Fuzzy logic, then, modifies Boolean logic to be arithmetical. The following meanings can be attached to the notation for the arithmetical hierarchy on formulas. These bases impart respectively a logical, an arithmetical, and a parsimonious character to the subject. Double false position arose in late antiquity as a purely arithmetical algorithm. Psellus also attributed arithmetical inventions by Diophantus to Pythagoras. The concept is essential for developing the arithmetical hierarchy and the analytical hierarchy. These type of sets can be classified using the arithmetical hierarchy. IEEE standard 1076.3 introduced signed and unsigned types to facilitate arithmetical operations on vectors.