Endless contouring . When we are young, surely at some point we hear some story or the other, maybe you have heard scary stories. Few things in mathematics are as magical as stories like "infinity".

 Endless contouring

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When we are young, surely at some point we hear some story or the other, maybe you have heard scary stories. Few things in mathematics are as magical as stories like "infinity". 

If I tell you that we have a bag, can we fill that bag or bag with limited items or unlimited? Of course you will say that we can only fill a bag with limited things. But I want you to assume that the bag and you have a set of numbers. Now if I ask you that you have to fill these numbers in the bag, will there ever be a point when this series will be completed? 

You will say "No, because it is infinite, so we will keep filling the bag, it will never end". But what if someone tells you that no, we can complete this process? There can come a point where the chain is complete and this is what a famous mathematician did. His name is George Cantor. This task was not easy for him because many people including the great mathematician Gauss were "against Cantor's theory". 

George Cantor (Georg Cantor was a mathematician, his life span is 1845-1918). 

Kantor's family was very much associated with music, so it was believed that Kantor's mathematical works also contained romantic songs. As it is a common observation that some intelligent people have strange things or even a half-interesting quirk in them. Now listen to Cantor, Cantor thought that what is Shakespeare's work is not Shakespeare's, it was written by Francis Bacon, and it seems that Cantor was also very sure of it. It is strange that this may be the reason that many people have blown up some things regarding Shakespeare that Shakespeare has cleaned his hands on the work of others. 

Kantor believed in one more thing and it's interesting and you will find it interesting too. Cantor believed that God was guiding him, that God was giving him help and instructions in the mathematical work that Cantor wanted to accomplish. And you also know that when a person reveals such things, other people make fun of them. Kantoor also faced such problems and more than that he was also facing depression. Depression that consumed much of his intellectual energy. 

Kantor used to encounter the evil impacts of demoralization for a really long time, considering the way that Kantor should be admitted to the center, distress has been going on for several years. The shapes would be invigorated and when they would get some help, they would return to their work. Kantoor used to say regarding this series that downturn has incredibly solidified his psychological state and newness. In those days misery was not dealt with like it is today. These days, the treatment of discouragement is pricey.

Cantor's greatest achievement or work is said to be his rejection of infinity. And they connected with infinity as if nothing had happened before. 

Kantor put forward two principles regarding infinity. 

1) We can talk about “complete infinity”, we are right to talk about complete infinity. 

But your question should be, what is this complete infinity? What is this concept? As we have already known the example of the bag, how will the process of filling the bag be completed when there is infinity? 

No one doubted that potential is a concept of infinity. Now Kantor made a distinction and battle between potential infinity and absolute infinity. As you have read before. From the example of the bag. Suppose we have a set of natural numbers, the potential infinity class believed that infinity would appear in it. 

N = { 1,2,3,4,5,6.......... 

This bracket will not be closed. But what did Kantor do? Kantor said no. You can turn it off by doing this. 

N={1,2,3,4.........}

In Kantor's view, this is complete infinity. When the concept of total infinity became widespread, the great mathematician of the time, Gauss, heard about it. Gauss believed in infinity that the chain could never be complete or end, so how could he believe that he did not believe in the concept of absolute infinity". Therefore, absolute infinity and potential infinity are opposed. The concept of complete infinity also seems strange when a person thinks carefully that there is infinity and it is complete, you say. And many strange things also come out of it, I will mention an example again. 

The second principle presented by Kantor. It was that "two sets have the same cardinality when their members are mutually exclusive."For example, you have five fingers on your hand. Now suppose you don't have a counting system. How can you tell whether the fingers on both hands are equal or not? 

Yes of course, you will touch the fingers of your right and left hand one by one and you will know. This is what Kontor wants to say that if all the fingers of the hands can be matched one by one, then they have a cardinality. And if there is no match then no. Now if you have considered then you will say that the set of fingers is limited. Absolutely correct. Cantor wanted to apply the concept of semi-cardinality universally, he said why not do one-to-one matching on infinite sets. So what's up? And why don't we see it next time.