Abstract. Systems of linear equations, called flexible systems, with coefficients having uncertainties of type o (.) or O (.) are studied. In some cases an exact solution may not exist but a general theorem that guarantees the existence of an admissible solution, in terms of inclusion, is presented. This admissible solution is produced by Cramer's Rule; depending on the size of the uncertainties appearing in the matrix of coefficients and in the constant term vector some adaptations may be needed.
Neutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized.
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