INFINITY - AN ILLUSION OR A REALITY ?

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 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 not as much know about physics but my little curiosity always wondered me and read physics about this. If I want to give you a simple proof  see how as Euclid give for the set of prime numbers is an infinite set. Now came to some mathematical figure The first figure came to my mind was sphere, If I consider the whole space is infinte dimensional sphere then its not give me a general idea. That's stop me there.

      If I start with simpleset  idea that is any number set ex- Natural, Rational,... . In college when I read about countable and uncountable set then I understand  the main fundamental the differnce between the following two, "Infinitely very large number set which is bounded where I / you want" and " Any Infinite set (Isomorphic to Set of Integers)", the differnce is simple both has large values but still after consideration one is end another is not end, may be most simpleest Idea but the beautiful think I observe here, what's like me most here is although the consideration set as long as we want to go and second one with also same like. So this example I thought a base of proof we can't reach at infinity if we then its also finite. 

        In mathematics we distinguish all by "Aleph null / Aleph one / Infinity ", " Aleph null () is the smallest infinte number, it's denoted the cardinallity of Natural Numbers " , "Aleph one () is next infinite cardinallity of countable infinite number" , and " infinity". In mathematics there is a concept of "Aleph number" I am going to deep in it, you just Google it. Main thing that I try to told you that we have different kind of infinity in mathematics, In one sense you see that sequence of aleph number strictly increasing so one might infinity increse time to time as more we gather knowledge about it.

        Now lastly I mention all I say upto now its on real line just think if we increase dimension thought about same in higher dimension where its reach ??

        One key possible is if you some how reach at the end you found out then its circular means the starting point and the end point is same, like a famous saying " Ant hi prarambh hai (means something where its end a new start froms there".

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