November 21, 2016 Monday

Bedtime Story 


Cardinality of a Set

To show the collection of elements in a set, curly brackets are used like this {}.

So we can show the set of prime numbers as:

P = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…}

By the way, it is a proven fact that the sequence of primes is never ending.

In other words, the number of primes is infinite.

The proof is rather simple and even you can think of it if you dare to give it a try.

The number of members in a set is called its cardinality.

For example, if P = {2, 3, 5, 7}, then its cardinality would be 4.

The cardinality of a set is represented by 2 vertical bars.

So |P| = 4.

This is the basics of set theory or how set theory was understood till Cantor came upon the stage.

Cantor started publishing his original mathematical works from 1874 after his marriage when he was 29 years old and was on his way to becoming a full Professor at the University of Halle.

Just as an aside, Cantor was one of the few geniuses that I am aware of who not only went on to reproduce to have 6 children but was also a firm believer of God.

Not only that, Cantor used or rather believed his mathematical work on infinite and infinities as proof of the existence of God.

The Church on the other hand saw his work as a serious assault on the idea of a unique and absolutely infinite God.

Religiosity was not uncommon (in fact, it was rather common) among mathematicians specially those who came before the 1900s.

Before his work on set theory starting in 1874, Cantor had started out with number theory including his thesis topic and later to analysis (or calculus).

He was given a challenge by his colleague Eduard Heine to come up with the solution to the problem of the uniqueness of the representation of a function by trigonometric series.

It was an open problem that had remained unsolved and eluded even mathematical giants such as Bernhard Riemann Peter Dirichlet and many more.

(He went on to publish 10 papers on number theory.)

It was while working on this problem that Cantor’s brain was struck with the idea of transfinite.

You may wonder what the word transfinite means.

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