devotion & mathematics

                                                                                                                                    P-Test for series :  Statement & Proof                                                           Back                                                                               ...

   https://youtu.be/7wb85EwAMRE?si=kCE0Lzdn0dLEF0mi Here in this page, I gave you proofs of some results regarding closed sets. Result 1: The sets N,W and Z are closed. Result 2: The set Q of rational numbers is not closed. Result 3: If a point p is a limit point of a nonempty set A then each neighborhood contains infinitely many points of A. Result 4: Union of arbitrary family of closed sets is not closed. Here we see their proofs. RESULT 1: The set N of natural numbers is closed. PROOF : RESULT 2: The set Q of rational numbers is not closed PROOF :  RESULT 3:  If a point p is a limit point of a nonempty set A then each                                                          neighborhood  contains infinitely many points of A. PROOF:  RESULT 4:    Union of arbitrary family of closed sets is not closed....