February 21, 2017 Tuesday

Bedtime Story 

Next Hyperoperation After Exponentiation is Tetration

Simple examples will clarify what hyperoperation means.

For example, what can be more primitive method of compounding a number x than adding a one to it and making it x + 1?

That would be a successor function.

The next primitive operator is addition.

Addition operation merely specifies the number of times 1 needs to be added to x to get the next value of x.

Multiplication follows next as it defines the number of times a number must be added to itself.

Exponentiation is the next in this hierarchy of hyperoperations that defines the number of times a number is to be multiplied to itself.

After exponentiation, the next hyperoperation is called tetration or hyper-4.  

Tetration is defined as iterated exponentiation.

Let us see how they can be beautifully represented with symbols without using so many useless words.

Succession:

a’ = a + 1

Addition:

a + n = a + (1 + 1 + 1 +…+ 1) where n copies of 1 are added to a.

Multiplication:

a . n  = a + a +…+ a  where n copies of a are combined by addition   

Exponentiation:

aⁿ = a x a x…x a where n copies of a are combined are combined by multiplication

Tetration:

ⁿa = a^a..a where n copies of a are combined by exponentiation, from right to left.

I could not write the “a”_s and the dots the way I wanted to, as each a and each dot should be written exponentially to the one left of it.

This above operation is the n^th tetration of a.  

Perhaps it will be better if I can you a picture of it.

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

                              

Good night mon ami and my fellow cousin ape.

                   

  

                

             

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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, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg