  In this paper possible completion $^*R_{d}$ of the Robinson non-archimedean
field $^*R$ constructed by Dedekind sections. Given an class of analytic
functions of one complex variable $f \in C[z]$,we investigate the arithmetic
nature of the values of $f$ at transcendental points $e^{n}$. Main results are:
1) the both numbers $e+\pi$ and $e\pi$ are irrational, 2) number $e^{e}$ is
transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem
is obtainedNon conservative extensions of the canonical nonstandard analysis
also is considered.
