Some algebraic properties of parts of real numbers
Authors:


AMS Classification:

11A99, 11A67

Keywords:

additive real group, addition, additive real set, bounded group, decimal and integer part of real numbers, symmetric real set, subtractive real set, decimal group, generalized division algorithm

Abstract:

The parts of real numbers were introduced and studied in [2] and [3] by M.H. Hooshmand. In this paper, we first discuss parts of real numbers and give another proof for the generalized division algorithm introduced in [3]. Then we focus on addition of two real numbers as a new binary operation in . In fact, addition of real numbers is decimal part of their ordinary addition denoted by . We show that is a semigroup and determine its subgroups (subsets which are groups with ). We call them bounded groups, because they are subsets of . Finally, we discuss the relations between bounded groups and subgroups of the additive real group and its quotient groups.

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Vol. 3 (11), 2008
