Valuation Theory. Part I

In the article we introduce a valuation function over a field [1]. Ring of non negative elements and its ideal of positive elements have been also defined. The notation and terminology used here have been introduced in the following We use the following convention: x, y, z, s are extended real numbers, i is an integer, and n, m are natural numbers. The following propositions are true: (1) If x = −x, then x = 0. (2) If x + x = 0, then x = 0.