과제 연습문제 풀이
수학이야기/Calculus
2020. 4. 22. 15:16
17. A function continuous at only one point Let $$f(n)=\begin{cases}x, & \mbox{if }x \mbox{ is a rational } \\0, & \mbox{if }x\mbox{ is irrational}\end{cases}$$ a. Show that $ƒ$ is continuous at $x = 0.$ b. Use the fact that every nonempty open interval of real numbers contains both rational and irrational numbers to show that ƒ is not continuous at any nonzero value of $x$. 18. The Dirichlet ru..
