The number defined by
considered by L. Euler (1740). Its existence follows from the fact that the sequence
is monotone increasing and bounded from above. The number-theoretic nature of the Euler constant has not been studied; it is not even known (1988) whether it is a rational number or not.
In fact, a relation
holds, cf. [a1], Chapt. 22.5.
|[a1]||G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Chapts. 5; 7; 8|
Euler constant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_constant&oldid=17956