MATH MAANIAC

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...

                                        GOLDBACH FUNCTION                                          Goldbach Conjecture is one of the famous conjecture in mathematics from many of years, mathematicians are still try to solve this till the time of conjecture discovered. Try to solve this famous conjecture mathematicians are discovered many new things related to this conjecture some of are proved. We seen mathematicians discovered many another versions of Goldbach Conjecture like pictorial form and graph form and computer program also. Today in the time many computer programs  proved that Goldbach Conjecture is true upto a highest integer.                                        ...

  A POINT TO A SPACE                   From after our birth to at before of our death what we saw outside us really very usual things but a mathematician eye always capture the beauty on it that's like a floating river and you flow within it . I remember when travel to college via local trains I saw skylines, clouds, lands, electric polls and others. Thats obviously usual things I belive who travel everyday saw this, but what I found interesting in this is everything have a proper shape and as required shape can be big or small not only that at the end to connect with one to one beautifully . If you not familier with such things I give you an usual example like you saw a book it has six sides with maximum three different areas in six sides. But this similar concepts varies and make it more interesting when add up differet kind of shape together. As a mathematician or as a seeker every new thing that we saw in our usual routine thats cha...