Algebraic Structure of Floating-Point Numbers
The aim of the study is to investigate the possibility of constructing an algebraic structure on the set of floating-point real numbers. The objectives are to investigate the structure of these numbers and the operations on them. It is assumed that an algebraic structure in the form of a group on a given set cannot be constructed. The proof of this hypothesis is based on checking the implementation of the laws of commutativity, associativity and distributivity for addition and multiplication operations. The results show that the laws of associativity and distributivity do not hold; this confirms the hypothesis and suggests that it is impossible to construct an algebraic structure on the set of numbers under consideration with these operations of a level higher than commutative algebra.