## Solutions to Real Analysis: A Long-Form Mathematics Textbook Chapter 3

Exercise 3.1 Solution: Let $\e=0.001$. Because $(a_n)$ converges to $0.001$, there exist $N$ such that for all $n> N$ we have\[|a_n-0.001| < 0.001,\]\[\Longrightarrow -0.001 < a_n- 0.001 < 0.001,\]\[\Longrightarrow 0<…