MATH MAANIAC

                NON-EUCLIDEAN GEOMETRY                  Every mathematics student to professor everyone heard the name of Euclid. He is famous for his contribution to the mathematics. One of his great contribution is Euclidean geometry. That we study whole our school life, that all based  on Euclid postulate and axioms that he write on his famous book "The Elements", that book has13 chapters based on his geometry.     And the great thing you know before 19th century mathematicians believe that Euclid geometry is god's word so no another geometry not exist, and but some mathematicians are believe some of Euclid postulate is can derive from other, so some are trying to prove but many tries and fail.      In 19th century  János Bolyai  and  Nikolai Ivanovich Lobachevsky  (separately) thought that instead of proving one of them imply from another we can mak...

                  TOPOLOGY - KING OF MATHEMATICS           From our childhood we are studying geometry, there we are studying different shapes and objects and their properties like area and many. Although in mathematics we are not bounded by dimension so we make any dimensional object and study it. By studying this in higher dimension we know more about real world and we more understand more pattern, this patterns are always in front of us but we have to find this.          Although we are saying in any dimension we are able work in any objects is it not that if we choose any arbitrary shape its sometimes difficult to study this formally.          Many days earlier I am familiar with another branch of mathematics there we don't have this boundary. Although by doing these process we have to make our geometry deform or properly say we not that much focus on geometry...

Solution of MS -2019, 3-4, PROBLEM 6             NOTE- Solution given here is not published but another version of proof that published in solution of this problem.  

  INTRODUCTION -    It is say that "If you don't  know the basic of any subject , you doesn't know anything about this subject".  As example "If you wish to build a building but the base of the building is not strong, then how the building is strong ?" In mathematics the base is "Analysis", the most fundamental part of mathematics. Many of  my reader may be familiar with "Real Analysis", "Complex Analysis" and many analytical concept we study in mathematics. If you are not familiar with this don't worry and if you someone who first ever listen about "ANALYSIS",  I promised you from start to the end of this blog is a great journey for you and it's gives your imagination a challenge to think. I request everyone who read this blog to read this without any pre-assumption and enjoy the journey.                   ANALYSIS  - Now you might be wonder and curious to know about " What is...

 Infinity - An Illusion OR A Reality?        I belive many people have this curiosity that Infinity- either it is a reality or its an illusion. This blog is not a answer of this mysterious question, but rather my opinion on infintity, although I never conclude that its not a reality or its a illusion, as a mathematecian I strongly belive everything I say must be strong base, I request every readers to comment their valueable opinions on Infinity / or if you have any conclusion then, Why?  INFINTY        The thought of  Infinity first came to my mind when I am in class 11, I am curious about the Universe, every time still now  when I closed my eyes and try to think about expansion of universe I am shocked, I am always wondered what is outside because the more we go outside its again expand where its end still a Question and the biggest question is  " If there is an end then what after next ?" Althogh I am a mathematician no...

  Russell's Paradox                   Last few days ago I wished to do the proof of " Cantor's Theorem ", although I am familier with this theorem from my first year of college, I am not abel to recall the exact proof, so I thought to do just elaborate what its exactly say and step by step go . If you not familier with " Cantor's Theorem " I stated for you, " There is no surjective mapping from any set onto the power of that set (set of all subsets of the choosen set) " . One thing first click to my mind by the property of cardinallity of a set, that if the set contain n elements then power set of choosen set contain    2 n  element. If you try to imagine this mapping you see to be surjective every element of power of set of the set goes to an element of the set (may not unique) and also keep in mind that to be well-defined mapping one element of the set must be go to a unique element of the power set of the set , so if we...