So I got this problem from my professor. For the first question, I've tried to wrote m as n or (n+1) (because m was supposedly greater than or equal to N, which was a part of n. Correct me if I'm wrong) , but still can't find a solution. And for the second question, I don't even know where to start.
(I'm sorry I can't write down the question properly with mathjax)
- (∀n∈ℕ)(∃N∈ℕ)(∀m∈ℕ)(m≥N → |(1+(1/m))^m) - e|<(1/n))
- (∀x∈ℚ)(∃n∈ℕ)(∀N∈ℕ)(∃m∈ℕ)(m≥N & |(1+(1/m))^m - x|≥(1/n))