1. The problem statement, all variables and given/known data Show that Euler's constant is 0 < [tex]\gamma[/tex] < 1 2. Relevant equations According to my book, [tex]\gamma[/tex] = lim((1+1/2+....+1/n) - log n) as n approaches infinity 3. The attempt at a solution At first glance I was thinking about proving by contradiction. First I assume [tex]\gamma[/tex] is equal to 0. Then I will get lim(1+1/2+....+1/n) = lim (log n) as n approaches infinity. However 1+1/2+....+1/n is a harmonic series which diverges, so the equality does not hold. So [tex]\gamma[/tex] does not equal 0. Next I assume [tex]\gamma[/tex] is less than 0. Since log function never yields negative result, this implies that lim(1+1/2+....+1/n) < lim(log n) as n approaches infinity. Again due to the divergent nature of harmonic series, the inequality does not hold. These are all I have for now. ================================= I feel I have logic error in the attempt to solve the problem, and I hope that someone will give me a hint on the correct solution.