Math 431 - Real Analysis I Solutions to Homework due.
Homework (20%), Midterm1 (20%), Midterm2 (20%), Final (40%). Note that you must pass your final in order to pass the course. For more information, click Course Syllabus; About having fun with some of math papers. Interesting math papers will be added here! Infinitely many units; Construction of the Real numbers By Cauchy sequences and By.
Mathematics I Objectives of the course and intended learning outcomes (competences) Student learns the basic concepts of mathematical analysis such as limit, continuity, derivative and integral of real functions of one real variable, numerical and function series, and continuity and differentiation of real functions of several real variables.
A metric space is called complete if every Cauchy sequence converges to a limit. Already know: with the usual metric is a complete space. Theorem. with the uniform metric is complete. Proof. Let be a Cauchy sequence in the sequence of real numbers is a Cauchy sequence (check it!). Since is a complete space, the sequence has a limit.