2 papers
math.NT2016
Diophantine approximation with improvement of the simultaneous control of the error and of the denominator
Abdelmadjid Boudaoud
In this work we proof the following theorem which is, in addition to someother lemmas, our main result:\noindent \textbf{theorem}. Let$\ X=\{ ( x\_{1}\text{, }%t\_{1}) \text{, }( x…
math.LO2016
A nonstandard proof for Szpilrajn's theorem
Abdelmadjid Boudaoud
Recall that Szpilrajn (1930) ([4], [5]) states that on a given set, any partial order can be extended to a total order on the same set. In this work we give, in the context of the…