November 29, 2016 Tuesday

Bedtime Story 

Cantor Defends His Ideas

After this 1874 paper, in a span of five years between 1879 and 1884 Cantor published 6 papers of which the 5^th paper was most significant.

This 5^th paper was titled “Foundations of a General theory of Aggregates”.

Already a lot of hostility and aversion was building up against Cantor’s ideas by the established professors at the helm of which was his own mentor Kronecker.

Kronecker found the concept of multiple infinites to be preposterous, as that would eventually lead to such insidious paradoxes that would destroy the foundations of mathematics.

Cantor would have none of it.

He had to pursue logic and reason and see where it took him; if it ended up in paradoxes then so be it.

In this fifth paper of the series that he published in 1883, he was not only laying down the foundations of set theory but was also defending himself from the belligerent attacks that were being hurled at him.

In this paper, he carefully began by defining the concept of well-ordered sets and ordinal numbers (order types of well ordered sets).

Then we went on to demonstrate how transfinite numbers are not something extraordinary, but merely an extension of natural numbers.

In this paper, Cantor also defined the rules of addition and multiplication for the cardinal and ordinal numbers.        

These were formidable papers in the sense that they were challenging the long standing beliefs of the existing establishment.

Yet it has the first 1874 paper that was published in the Crelle’s Journal that was most revolutionary.

It laid the background for his dealing with the notion of Euclidean space or real coordinate space of n dimensions that is denoted by the symbol Rⁿ.

  

Let me deal with the Euclidean space in the nights to come.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.in/

                              

Good night and my fellow cousin ape.

         

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, may I suggest this large collection of Kids Songs:

https://www.youtube.com/channel/UCMX11Z5SJQ3kgwSsFJLRIcg