devotion & mathematics

   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....

 PROOFS OF FEW RESULTS  1:                    Here we are going to see the proofs of some results what we know. They are   1.  Intersection of an infinite collection of open sets is not open.  2. The set N of natural numbers is not open.  3.  Every neighborhood is an open set.  4.  Union of any collection of open sets is open. Now come to proofs : 1. INTERSECTION OF AN INFINITE COLLECTION OF OPEN SETS IS NOT OPEN : PROOF : 2. THE SET N OF NATURAL NUMBERS IS NOT OPEN: PROOF :  3. EVERY NEIGHBORHOOD IS AN OPEN SET : PROOF : 4. UNION OF ANY COLLECTION OF OPEN SETS IS OPEN : PROOF : people also ask         * what is an interior point * what is an open set        * what is a neighborhood                * what is extended real number                      *...